← A level balance is an equation · Find Two Unknowns from Sum and Difference

A level balance is an equation · 12 practice problems

1.OA.D.73.OA.A.44.NBT.B.5

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Variant 1 easy

A balance scale is level. If one green marble weighs $15\ \text{g}$ and one yellow marble weighs $10\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 8 green marbles on one side and 3 red plus 6 yellow on the other. Green marbles weigh 15 g and yellow ones 10 g. We need the weight of one red marble.

Givens

Left pan: 8 green marbles at 15 g each.
Right pan: 3 red marbles and 6 yellow at 10 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 8 green marbles, each 15 g. Multiply to get the total weight the right pan must match.

8 \times 15 = 120 \text{ g}

The right side has to come to 120 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 6 yellow marbles are known: each is 10 g. Add them to see how much weight is already accounted for.

6 \times 10 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 3 red marbles) must weigh the same 120 g as the left pan. So the 3 red marbles together weigh the difference.

120 - 60 = 60 \text{ g}

All the reds together are 60 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 3 equal red marbles share that 60 g. Guess a red weight and check: if red is 20 g, then 3 x 20 = 60, and 60 + 60 = 120, which matches the left pan exactly.

3 \times 20 = 60,\quad 60 + 60 = 120

One red marble is 20 g.

Answer: 20 g

4 · Reviewdoes it hold up?

Total both sides with 20 g reds: left is 120 g, right is 3 x 20 + 6 x 10 = 60 + 60 = 120 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (20 g against 10 g), which fits: the right pan needs 9 marbles to match the left pan's 8.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 2 easy

A balance scale is level. If one green marble weighs $18\ \text{g}$ and one yellow marble weighs $14\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 7 green marbles on one side and 4 red plus 5 yellow on the other. Green marbles weigh 18 g and yellow ones 14 g. We need the weight of one red marble.

Givens

Left pan: 7 green marbles at 18 g each.
Right pan: 4 red marbles and 5 yellow at 14 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 7 green marbles, each 18 g. Multiply to get the total weight the right pan must match.

7 \times 18 = 126 \text{ g}

The right side has to come to 126 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 5 yellow marbles are known: each is 14 g. Add them to see how much weight is already accounted for.

5 \times 14 = 70 \text{ g}

70 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (70 g of yellow plus 4 red marbles) must weigh the same 126 g as the left pan. So the 4 red marbles together weigh the difference.

126 - 70 = 56 \text{ g}

All the reds together are 56 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 4 equal red marbles share that 56 g. Guess a red weight and check: if red is 14 g, then 4 x 14 = 56, and 70 + 56 = 126, which matches the left pan exactly.

4 \times 14 = 56,\quad 70 + 56 = 126

One red marble is 14 g.

Answer: 14 g

4 · Reviewdoes it hold up?

Total both sides with 14 g reds: left is 126 g, right is 4 x 14 + 5 x 14 = 56 + 70 = 126 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (14 g against 14 g), which fits: the right pan needs 9 marbles to match the left pan's 7.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 3 easy

A balance scale is level. If one green marble weighs $20\ \text{g}$ and one yellow marble weighs $15\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 6 green marbles on one side and 3 red plus 4 yellow on the other. Green marbles weigh 20 g and yellow ones 15 g. We need the weight of one red marble.

Givens

Left pan: 6 green marbles at 20 g each.
Right pan: 3 red marbles and 4 yellow at 15 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 6 green marbles, each 20 g. Multiply to get the total weight the right pan must match.

6 \times 20 = 120 \text{ g}

The right side has to come to 120 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 4 yellow marbles are known: each is 15 g. Add them to see how much weight is already accounted for.

4 \times 15 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 3 red marbles) must weigh the same 120 g as the left pan. So the 3 red marbles together weigh the difference.

120 - 60 = 60 \text{ g}

All the reds together are 60 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 3 equal red marbles share that 60 g. Guess a red weight and check: if red is 20 g, then 3 x 20 = 60, and 60 + 60 = 120, which matches the left pan exactly.

3 \times 20 = 60,\quad 60 + 60 = 120

One red marble is 20 g.

Answer: 20 g

4 · Reviewdoes it hold up?

Total both sides with 20 g reds: left is 120 g, right is 3 x 20 + 4 x 15 = 60 + 60 = 120 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (20 g against 15 g), which fits: the right pan needs 7 marbles to match the left pan's 6.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 4 easy

A balance scale is level. If one green marble weighs $22\ \text{g}$ and one yellow marble weighs $18\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 9 green marbles on one side and 3 red plus 6 yellow on the other. Green marbles weigh 22 g and yellow ones 18 g. We need the weight of one red marble.

Givens

Left pan: 9 green marbles at 22 g each.
Right pan: 3 red marbles and 6 yellow at 18 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 9 green marbles, each 22 g. Multiply to get the total weight the right pan must match.

9 \times 22 = 198 \text{ g}

The right side has to come to 198 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 6 yellow marbles are known: each is 18 g. Add them to see how much weight is already accounted for.

6 \times 18 = 108 \text{ g}

108 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (108 g of yellow plus 3 red marbles) must weigh the same 198 g as the left pan. So the 3 red marbles together weigh the difference.

198 - 108 = 90 \text{ g}

All the reds together are 90 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 3 equal red marbles share that 90 g. Guess a red weight and check: if red is 30 g, then 3 x 30 = 90, and 108 + 90 = 198, which matches the left pan exactly.

3 \times 30 = 90,\quad 108 + 90 = 198

One red marble is 30 g.

Answer: 30 g

4 · Reviewdoes it hold up?

Total both sides with 30 g reds: left is 198 g, right is 3 x 30 + 6 x 18 = 90 + 108 = 198 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (30 g against 18 g), which fits: the right pan needs 9 marbles to match the left pan's 9.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 5 medium

A balance scale is level. If one green marble weighs $24\ \text{g}$ and one yellow marble weighs $21\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 7 green marbles on one side and 4 red plus 4 yellow on the other. Green marbles weigh 24 g and yellow ones 21 g. We need the weight of one red marble.

Givens

Left pan: 7 green marbles at 24 g each.
Right pan: 4 red marbles and 4 yellow at 21 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 7 green marbles, each 24 g. Multiply to get the total weight the right pan must match.

7 \times 24 = 168 \text{ g}

The right side has to come to 168 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 4 yellow marbles are known: each is 21 g. Add them to see how much weight is already accounted for.

4 \times 21 = 84 \text{ g}

84 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (84 g of yellow plus 4 red marbles) must weigh the same 168 g as the left pan. So the 4 red marbles together weigh the difference.

168 - 84 = 84 \text{ g}

All the reds together are 84 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 4 equal red marbles share that 84 g. Guess a red weight and check: if red is 21 g, then 4 x 21 = 84, and 84 + 84 = 168, which matches the left pan exactly.

4 \times 21 = 84,\quad 84 + 84 = 168

One red marble is 21 g.

Answer: 21 g

4 · Reviewdoes it hold up?

Total both sides with 21 g reds: left is 168 g, right is 4 x 21 + 4 x 21 = 84 + 84 = 168 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (21 g against 21 g), which fits: the right pan needs 8 marbles to match the left pan's 7.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 6 medium

A balance scale is level. If one green marble weighs $24\ \text{g}$ and one yellow marble weighs $28\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 5 green marbles on one side and 2 red plus 3 yellow on the other. Green marbles weigh 24 g and yellow ones 28 g. We need the weight of one red marble.

Givens

Left pan: 5 green marbles at 24 g each.
Right pan: 2 red marbles and 3 yellow at 28 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 5 green marbles, each 24 g. Multiply to get the total weight the right pan must match.

5 \times 24 = 120 \text{ g}

The right side has to come to 120 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 3 yellow marbles are known: each is 28 g. Add them to see how much weight is already accounted for.

3 \times 28 = 84 \text{ g}

84 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (84 g of yellow plus 2 red marbles) must weigh the same 120 g as the left pan. So the 2 red marbles together weigh the difference.

120 - 84 = 36 \text{ g}

All the reds together are 36 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 2 equal red marbles share that 36 g. Guess a red weight and check: if red is 18 g, then 2 x 18 = 36, and 84 + 36 = 120, which matches the left pan exactly.

2 \times 18 = 36,\quad 84 + 36 = 120

One red marble is 18 g.

Answer: 18 g

4 · Reviewdoes it hold up?

Total both sides with 18 g reds: left is 120 g, right is 2 x 18 + 3 x 28 = 36 + 84 = 120 g. Level, as stated.

Another way: A red marble is lighter than a yellow one (18 g against 28 g), which fits: the right pan needs 5 marbles to match the left pan's 5.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 7 medium

A balance scale is level. If one green marble weighs $28\ \text{g}$ and one yellow marble weighs $30\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 5 green marbles on one side and 4 red plus 2 yellow on the other. Green marbles weigh 28 g and yellow ones 30 g. We need the weight of one red marble.

Givens

Left pan: 5 green marbles at 28 g each.
Right pan: 4 red marbles and 2 yellow at 30 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 5 green marbles, each 28 g. Multiply to get the total weight the right pan must match.

5 \times 28 = 140 \text{ g}

The right side has to come to 140 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 2 yellow marbles are known: each is 30 g. Add them to see how much weight is already accounted for.

2 \times 30 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 4 red marbles) must weigh the same 140 g as the left pan. So the 4 red marbles together weigh the difference.

140 - 60 = 80 \text{ g}

All the reds together are 80 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 4 equal red marbles share that 80 g. Guess a red weight and check: if red is 20 g, then 4 x 20 = 80, and 60 + 80 = 140, which matches the left pan exactly.

4 \times 20 = 80,\quad 60 + 80 = 140

One red marble is 20 g.

Answer: 20 g

4 · Reviewdoes it hold up?

Total both sides with 20 g reds: left is 140 g, right is 4 x 20 + 2 x 30 = 80 + 60 = 140 g. Level, as stated.

Another way: A red marble is lighter than a yellow one (20 g against 30 g), which fits: the right pan needs 6 marbles to match the left pan's 5.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 8 medium

A balance scale is level. If one green marble weighs $30\ \text{g}$ and one yellow marble weighs $25\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 4 green marbles on one side and 2 red plus 2 yellow on the other. Green marbles weigh 30 g and yellow ones 25 g. We need the weight of one red marble.

Givens

Left pan: 4 green marbles at 30 g each.
Right pan: 2 red marbles and 2 yellow at 25 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 4 green marbles, each 30 g. Multiply to get the total weight the right pan must match.

4 \times 30 = 120 \text{ g}

The right side has to come to 120 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 2 yellow marbles are known: each is 25 g. Add them to see how much weight is already accounted for.

2 \times 25 = 50 \text{ g}

50 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (50 g of yellow plus 2 red marbles) must weigh the same 120 g as the left pan. So the 2 red marbles together weigh the difference.

120 - 50 = 70 \text{ g}

All the reds together are 70 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 2 equal red marbles share that 70 g. Guess a red weight and check: if red is 35 g, then 2 x 35 = 70, and 50 + 70 = 120, which matches the left pan exactly.

2 \times 35 = 70,\quad 50 + 70 = 120

One red marble is 35 g.

Answer: 35 g

4 · Reviewdoes it hold up?

Total both sides with 35 g reds: left is 120 g, right is 2 x 35 + 2 x 25 = 70 + 50 = 120 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (35 g against 25 g), which fits: the right pan needs 4 marbles to match the left pan's 4.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 9 hard

A balance scale is level. If one green marble weighs $32\ \text{g}$ and one yellow marble weighs $24\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 6 green marbles on one side and 2 red plus 4 yellow on the other. Green marbles weigh 32 g and yellow ones 24 g. We need the weight of one red marble.

Givens

Left pan: 6 green marbles at 32 g each.
Right pan: 2 red marbles and 4 yellow at 24 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 6 green marbles, each 32 g. Multiply to get the total weight the right pan must match.

6 \times 32 = 192 \text{ g}

The right side has to come to 192 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 4 yellow marbles are known: each is 24 g. Add them to see how much weight is already accounted for.

4 \times 24 = 96 \text{ g}

96 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (96 g of yellow plus 2 red marbles) must weigh the same 192 g as the left pan. So the 2 red marbles together weigh the difference.

192 - 96 = 96 \text{ g}

All the reds together are 96 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 2 equal red marbles share that 96 g. Guess a red weight and check: if red is 48 g, then 2 x 48 = 96, and 96 + 96 = 192, which matches the left pan exactly.

2 \times 48 = 96,\quad 96 + 96 = 192

One red marble is 48 g.

Answer: 48 g

4 · Reviewdoes it hold up?

Total both sides with 48 g reds: left is 192 g, right is 2 x 48 + 4 x 24 = 96 + 96 = 192 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (48 g against 24 g), which fits: the right pan needs 6 marbles to match the left pan's 6.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 10 hard

A balance scale is level. If one green marble weighs $36\ \text{g}$ and one yellow marble weighs $20\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 5 green marbles on one side and 4 red plus 3 yellow on the other. Green marbles weigh 36 g and yellow ones 20 g. We need the weight of one red marble.

Givens

Left pan: 5 green marbles at 36 g each.
Right pan: 4 red marbles and 3 yellow at 20 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 5 green marbles, each 36 g. Multiply to get the total weight the right pan must match.

5 \times 36 = 180 \text{ g}

The right side has to come to 180 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 3 yellow marbles are known: each is 20 g. Add them to see how much weight is already accounted for.

3 \times 20 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 4 red marbles) must weigh the same 180 g as the left pan. So the 4 red marbles together weigh the difference.

180 - 60 = 120 \text{ g}

All the reds together are 120 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 4 equal red marbles share that 120 g. Guess a red weight and check: if red is 30 g, then 4 x 30 = 120, and 60 + 120 = 180, which matches the left pan exactly.

4 \times 30 = 120,\quad 60 + 120 = 180

One red marble is 30 g.

Answer: 30 g

4 · Reviewdoes it hold up?

Total both sides with 30 g reds: left is 180 g, right is 4 x 30 + 3 x 20 = 120 + 60 = 180 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (30 g against 20 g), which fits: the right pan needs 7 marbles to match the left pan's 5.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 11 hard

A balance scale is level. If one green marble weighs $40\ \text{g}$ and one yellow marble weighs $30\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 3 green marbles on one side and 2 red plus 2 yellow on the other. Green marbles weigh 40 g and yellow ones 30 g. We need the weight of one red marble.

Givens

Left pan: 3 green marbles at 40 g each.
Right pan: 2 red marbles and 2 yellow at 30 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 3 green marbles, each 40 g. Multiply to get the total weight the right pan must match.

3 \times 40 = 120 \text{ g}

The right side has to come to 120 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 2 yellow marbles are known: each is 30 g. Add them to see how much weight is already accounted for.

2 \times 30 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 2 red marbles) must weigh the same 120 g as the left pan. So the 2 red marbles together weigh the difference.

120 - 60 = 60 \text{ g}

All the reds together are 60 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 2 equal red marbles share that 60 g. Guess a red weight and check: if red is 30 g, then 2 x 30 = 60, and 60 + 60 = 120, which matches the left pan exactly.

2 \times 30 = 60,\quad 60 + 60 = 120

One red marble is 30 g.

Answer: 30 g

4 · Reviewdoes it hold up?

Total both sides with 30 g reds: left is 120 g, right is 2 x 30 + 2 x 30 = 60 + 60 = 120 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (30 g against 30 g), which fits: the right pan needs 4 marbles to match the left pan's 3.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Variant 12 hard

A balance scale is level. If one green marble weighs $45\ \text{g}$ and one yellow marble weighs $20\ \text{g}$ , how many grams does one red marble weigh? (Marbles of the same color have the same weight.)

Your answer

Show solution

1 · Understandwhat's really being asked

A level balance has 4 green marbles on one side and 3 red plus 3 yellow on the other. Green marbles weigh 45 g and yellow ones 20 g. We need the weight of one red marble.

Givens

Left pan: 4 green marbles at 45 g each.
Right pan: 3 red marbles and 3 yellow at 20 g each.
The scale is level.

Unknowns

The weight of one red marble.

Constraints

Marbles of the same colour weigh the same.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #1 Draw a Diagram#7 Identify Subproblems

Level means the two sides weigh the same, so the picture is really an equation. Total each side as far as it can be totalled, and what is missing has to make up the difference.

3 · Execute4 carry out the plan

1Weigh the left pan

#7 Identify Subproblems 4.NBT.B.5

The left pan has 4 green marbles, each 45 g. Multiply to get the total weight the right pan must match.

4 \times 45 = 180 \text{ g}

The right side has to come to 180 g as well.

2Weigh the known part of the right pan

#7 Identify Subproblems 4.NBT.B.5

On the right pan, the 3 yellow marbles are known: each is 20 g. Add them to see how much weight is already accounted for.

3 \times 20 = 60 \text{ g}

60 g of the right pan is yellow.

3Use the balance to set the two pans equal

#1 Draw a Diagram 1.OA.D.7

Because the scale is level, the right pan (60 g of yellow plus 3 red marbles) must weigh the same 180 g as the left pan. So the 3 red marbles together weigh the difference.

180 - 60 = 120 \text{ g}

All the reds together are 120 g.

4Guess and check the red marble weight

#6 Guess and Check 3.OA.A.4

The 3 equal red marbles share that 120 g. Guess a red weight and check: if red is 40 g, then 3 x 40 = 120, and 60 + 120 = 180, which matches the left pan exactly.

3 \times 40 = 120,\quad 60 + 120 = 180

One red marble is 40 g.

Answer: 40 g

4 · Reviewdoes it hold up?

Total both sides with 40 g reds: left is 180 g, right is 3 x 40 + 3 x 20 = 120 + 60 = 180 g. Level, as stated.

Another way: A red marble is heavier than a yellow one (40 g against 20 g), which fits: the right pan needs 6 marbles to match the left pan's 4.

Standardsmin grade 4

1.OA.D.7 Understand the meaning of the equal sign — Reading a level balance as the two sides being equal.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation — Finding one red marble's weight from the reds' total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Totalling each pan by multiplying count by weight.

💡Takeaway. A level scale is an equals sign you can see, so whatever is missing on one side has to fill the gap exactly.

Where next?

← Back to the problem: A level balance is an equation