← Combine part expressions into one expression · Decompose a Number into Parts and Factors

Combine part expressions into one expression · 12 practice problems

5.OA.A.25.OA.A.1

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 32 marbles

There are $8$ red marbles. There are $5$ more green marbles than red marbles. The number of yellow marbles is $7$ fewer than $3$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 8. Green is 5 more than red. Yellow is 7 fewer than 3 times green. We need how many yellow marbles there are.

Givens

Red: 8.
Green: 5 more than red.
Yellow: 7 fewer than 3 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'5 more than red' means add 5 to 8.

8 + 5 = 13

There are 13 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 3 times the green, then remove 7.

3 \times 13 = 39,\quad 39 - 7 = 32

There are 32 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 13 for (8 + 5) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

3 \times (8 + 5) - 7 = 32

One expression now records the whole chain of words.

Answer: 32 marbles

4 · Reviewdoes it hold up?

Read it back: 13 green is 5 more than 8 red, and 32 is 7 less than 3 x 13 = 39. Both sentences check out.

Another way: Without the parentheses the expression would mean 3 x 8 + 5 - 7 = 22, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 2 easy answer: 26 marbles

There are $12$ red marbles. There are $3$ more green marbles than red marbles. The number of yellow marbles is $4$ fewer than $2$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 12. Green is 3 more than red. Yellow is 4 fewer than 2 times green. We need how many yellow marbles there are.

Givens

Red: 12.
Green: 3 more than red.
Yellow: 4 fewer than 2 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'3 more than red' means add 3 to 12.

12 + 3 = 15

There are 15 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 2 times the green, then remove 4.

2 \times 15 = 30,\quad 30 - 4 = 26

There are 26 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 15 for (12 + 3) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

2 \times (12 + 3) - 4 = 26

One expression now records the whole chain of words.

Answer: 26 marbles

4 · Reviewdoes it hold up?

Read it back: 15 green is 3 more than 12 red, and 26 is 4 less than 2 x 15 = 30. Both sentences check out.

Another way: Without the parentheses the expression would mean 2 x 12 + 3 - 4 = 23, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 3 easy answer: 72 marbles

There are $15$ red marbles. There are $6$ more green marbles than red marbles. The number of yellow marbles is $12$ fewer than $4$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 15. Green is 6 more than red. Yellow is 12 fewer than 4 times green. We need how many yellow marbles there are.

Givens

Red: 15.
Green: 6 more than red.
Yellow: 12 fewer than 4 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'6 more than red' means add 6 to 15.

15 + 6 = 21

There are 21 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 4 times the green, then remove 12.

4 \times 21 = 84,\quad 84 - 12 = 72

There are 72 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 21 for (15 + 6) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

4 \times (15 + 6) - 12 = 72

One expression now records the whole chain of words.

Answer: 72 marbles

4 · Reviewdoes it hold up?

Read it back: 21 green is 6 more than 15 red, and 72 is 12 less than 4 x 21 = 84. Both sentences check out.

Another way: Without the parentheses the expression would mean 4 x 15 + 6 - 12 = 54, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 4 easy answer: 42 marbles

There are $10$ red marbles. There are $9$ more green marbles than red marbles. The number of yellow marbles is $15$ fewer than $3$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 10. Green is 9 more than red. Yellow is 15 fewer than 3 times green. We need how many yellow marbles there are.

Givens

Red: 10.
Green: 9 more than red.
Yellow: 15 fewer than 3 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'9 more than red' means add 9 to 10.

10 + 9 = 19

There are 19 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 3 times the green, then remove 15.

3 \times 19 = 57,\quad 57 - 15 = 42

There are 42 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 19 for (10 + 9) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

3 \times (10 + 9) - 15 = 42

One expression now records the whole chain of words.

Answer: 42 marbles

4 · Reviewdoes it hold up?

Read it back: 19 green is 9 more than 10 red, and 42 is 15 less than 3 x 19 = 57. Both sentences check out.

Another way: Without the parentheses the expression would mean 3 x 10 + 9 - 15 = 24, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 5 medium answer: 39 marbles

There are $16$ red marbles. There are $12$ more green marbles than red marbles. The number of yellow marbles is $17$ fewer than $2$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 16. Green is 12 more than red. Yellow is 17 fewer than 2 times green. We need how many yellow marbles there are.

Givens

Red: 16.
Green: 12 more than red.
Yellow: 17 fewer than 2 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'12 more than red' means add 12 to 16.

16 + 12 = 28

There are 28 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 2 times the green, then remove 17.

2 \times 28 = 56,\quad 56 - 17 = 39

There are 39 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 28 for (16 + 12) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

2 \times (16 + 12) - 17 = 39

One expression now records the whole chain of words.

Answer: 39 marbles

4 · Reviewdoes it hold up?

Read it back: 28 green is 12 more than 16 red, and 39 is 17 less than 2 x 28 = 56. Both sentences check out.

Another way: Without the parentheses the expression would mean 2 x 16 + 12 - 17 = 27, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 6 medium answer: 80 marbles

There are $18$ red marbles. There are $2$ more green marbles than red marbles. The number of yellow marbles is $20$ fewer than $5$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 18. Green is 2 more than red. Yellow is 20 fewer than 5 times green. We need how many yellow marbles there are.

Givens

Red: 18.
Green: 2 more than red.
Yellow: 20 fewer than 5 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'2 more than red' means add 2 to 18.

18 + 2 = 20

There are 20 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 5 times the green, then remove 20.

5 \times 20 = 100,\quad 100 - 20 = 80

There are 80 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 20 for (18 + 2) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

5 \times (18 + 2) - 20 = 80

One expression now records the whole chain of words.

Answer: 80 marbles

4 · Reviewdoes it hold up?

Read it back: 20 green is 2 more than 18 red, and 80 is 20 less than 5 x 20 = 100. Both sentences check out.

Another way: Without the parentheses the expression would mean 5 x 18 + 2 - 20 = 72, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 7 medium answer: 39 marbles

There are $20$ red marbles. There are $4$ more green marbles than red marbles. The number of yellow marbles is $9$ fewer than $2$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 20. Green is 4 more than red. Yellow is 9 fewer than 2 times green. We need how many yellow marbles there are.

Givens

Red: 20.
Green: 4 more than red.
Yellow: 9 fewer than 2 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'4 more than red' means add 4 to 20.

20 + 4 = 24

There are 24 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 2 times the green, then remove 9.

2 \times 24 = 48,\quad 48 - 9 = 39

There are 39 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 24 for (20 + 4) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

2 \times (20 + 4) - 9 = 39

One expression now records the whole chain of words.

Answer: 39 marbles

4 · Reviewdoes it hold up?

Read it back: 24 green is 4 more than 20 red, and 39 is 9 less than 2 x 24 = 48. Both sentences check out.

Another way: Without the parentheses the expression would mean 2 x 20 + 4 - 9 = 35, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 8 medium answer: 53 marbles

There are $14$ red marbles. There are $11$ more green marbles than red marbles. The number of yellow marbles is $22$ fewer than $3$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 14. Green is 11 more than red. Yellow is 22 fewer than 3 times green. We need how many yellow marbles there are.

Givens

Red: 14.
Green: 11 more than red.
Yellow: 22 fewer than 3 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'11 more than red' means add 11 to 14.

14 + 11 = 25

There are 25 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 3 times the green, then remove 22.

3 \times 25 = 75,\quad 75 - 22 = 53

There are 53 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 25 for (14 + 11) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

3 \times (14 + 11) - 22 = 53

One expression now records the whole chain of words.

Answer: 53 marbles

4 · Reviewdoes it hold up?

Read it back: 25 green is 11 more than 14 red, and 53 is 22 less than 3 x 25 = 75. Both sentences check out.

Another way: Without the parentheses the expression would mean 3 x 14 + 11 - 22 = 31, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 9 hard answer: 90 marbles

There are $22$ red marbles. There are $5$ more green marbles than red marbles. The number of yellow marbles is $18$ fewer than $4$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 22. Green is 5 more than red. Yellow is 18 fewer than 4 times green. We need how many yellow marbles there are.

Givens

Red: 22.
Green: 5 more than red.
Yellow: 18 fewer than 4 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'5 more than red' means add 5 to 22.

22 + 5 = 27

There are 27 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 4 times the green, then remove 18.

4 \times 27 = 108,\quad 108 - 18 = 90

There are 90 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 27 for (22 + 5) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

4 \times (22 + 5) - 18 = 90

One expression now records the whole chain of words.

Answer: 90 marbles

4 · Reviewdoes it hold up?

Read it back: 27 green is 5 more than 22 red, and 90 is 18 less than 4 x 27 = 108. Both sentences check out.

Another way: Without the parentheses the expression would mean 4 x 22 + 5 - 18 = 75, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 10 hard answer: 53 marbles

There are $25$ red marbles. There are $7$ more green marbles than red marbles. The number of yellow marbles is $11$ fewer than $2$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 25. Green is 7 more than red. Yellow is 11 fewer than 2 times green. We need how many yellow marbles there are.

Givens

Red: 25.
Green: 7 more than red.
Yellow: 11 fewer than 2 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'7 more than red' means add 7 to 25.

25 + 7 = 32

There are 32 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 2 times the green, then remove 11.

2 \times 32 = 64,\quad 64 - 11 = 53

There are 53 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 32 for (25 + 7) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

2 \times (25 + 7) - 11 = 53

One expression now records the whole chain of words.

Answer: 53 marbles

4 · Reviewdoes it hold up?

Read it back: 32 green is 7 more than 25 red, and 53 is 11 less than 2 x 32 = 64. Both sentences check out.

Another way: Without the parentheses the expression would mean 2 x 25 + 7 - 11 = 46, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 11 hard answer: 77 marbles

There are $28$ red marbles. There are $6$ more green marbles than red marbles. The number of yellow marbles is $25$ fewer than $3$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 28. Green is 6 more than red. Yellow is 25 fewer than 3 times green. We need how many yellow marbles there are.

Givens

Red: 28.
Green: 6 more than red.
Yellow: 25 fewer than 3 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'6 more than red' means add 6 to 28.

28 + 6 = 34

There are 34 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 3 times the green, then remove 25.

3 \times 34 = 102,\quad 102 - 25 = 77

There are 77 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 34 for (28 + 6) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

3 \times (28 + 6) - 25 = 77

One expression now records the whole chain of words.

Answer: 77 marbles

4 · Reviewdoes it hold up?

Read it back: 34 green is 6 more than 28 red, and 77 is 25 less than 3 x 34 = 102. Both sentences check out.

Another way: Without the parentheses the expression would mean 3 x 28 + 6 - 25 = 65, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.

Variant 12 hard answer: 63 marbles

There are $30$ red marbles. There are $8$ more green marbles than red marbles. The number of yellow marbles is $13$ fewer than $2$ times the number of green marbles. How many yellow marbles are there?

Show solution

1 · Understandwhat's really being asked

Red marbles number 30. Green is 8 more than red. Yellow is 13 fewer than 2 times green. We need how many yellow marbles there are.

Givens

Red: 30.
Green: 8 more than red.
Yellow: 13 fewer than 2 times green.

Unknowns

The number of yellow marbles.

Constraints

Yellow is defined through green, and green through red, so the order matters.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #5 Look for a Pattern

Each colour is built from the one before it, so work forwards: red to green, green to yellow. Then fold the two small expressions into one and see the parentheses the words were hiding.

3 · Execute3 carry out the plan

1Find the green marbles

#7 Identify Subproblems 5.OA.A.2

'8 more than red' means add 8 to 30.

30 + 8 = 38

There are 38 green marbles.

2Find the yellow marbles

#7 Identify Subproblems 5.OA.A.2

Take 2 times the green, then remove 13.

2 \times 38 = 76,\quad 76 - 13 = 63

There are 63 yellow marbles.

3Combine the parts into one expression

#5 Look for a Pattern 5.OA.A.1

Swapping 38 for (30 + 8) folds both steps into a single expression. The parentheses are what keep the addition happening before the multiplication.

2 \times (30 + 8) - 13 = 63

One expression now records the whole chain of words.

Answer: 63 marbles

4 · Reviewdoes it hold up?

Read it back: 38 green is 8 more than 30 red, and 63 is 13 less than 2 x 38 = 76. Both sentences check out.

Another way: Without the parentheses the expression would mean 2 x 30 + 8 - 13 = 55, which is not what the words say -- that is exactly what the brackets prevent.

Standardsmin grade 5

5.OA.A.2 Write simple expressions that record calculations with numbers — Recording each 'more than' and 'fewer than' as a calculation.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions and evaluate — Using parentheses so the combined expression keeps the right order.

💡Takeaway. When one amount is described through another, substitute it in -- and add the brackets that the sentence was implying all along.