← Moving things between two people leaves the total alone · Track a Quantity Through Changes

Moving things between two people leaves the total alone · 12 practice problems

6.EE.B.76.RP.A.3

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Variant 1 easy

Jia and Minho each had $18$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $4 : 5$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 18 candies each. After one gives some to the other, their counts are in the ratio 4 to 5. We want how many were given.

Givens

Each started with 18 candies.
Afterwards the ratio is 4 to 5.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

18 + 18 = 36

Still 36 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

4 to 5 means 9 equal parts of the 36.

36 \div 9 = 4

Each part is 4 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 4 of the 9 parts.

4 \times 4 = 16

Jia has 16 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

18 - 16 = 2

She gave away 2.

Answer: 2 candies

4 · Reviewdoes it hold up?

After the gift Jia has 16 and Minho 20: they add to 36 and stand in the ratio 4 to 5.

Another way: Following Minho instead -- he gains what Jia loses, so 18 plus the gift is 20 -- gives the same 2 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 2 easy

Jia and Minho each had $20$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $1 : 3$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 20 candies each. After one gives some to the other, their counts are in the ratio 1 to 3. We want how many were given.

Givens

Each started with 20 candies.
Afterwards the ratio is 1 to 3.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

20 + 20 = 40

Still 40 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

1 to 3 means 4 equal parts of the 40.

40 \div 4 = 10

Each part is 10 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 1 of the 4 parts.

10 \times 1 = 10

Jia has 10 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

20 - 10 = 10

She gave away 10.

Answer: 10 candies

4 · Reviewdoes it hold up?

After the gift Jia has 10 and Minho 30: they add to 40 and stand in the ratio 1 to 3.

Another way: Following Minho instead -- he gains what Jia loses, so 20 plus the gift is 30 -- gives the same 10 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 3 easy

Jia and Minho each had $24$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $1 : 2$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 24 candies each. After one gives some to the other, their counts are in the ratio 1 to 2. We want how many were given.

Givens

Each started with 24 candies.
Afterwards the ratio is 1 to 2.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

24 + 24 = 48

Still 48 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

1 to 2 means 3 equal parts of the 48.

48 \div 3 = 16

Each part is 16 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 1 of the 3 parts.

16 \times 1 = 16

Jia has 16 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

24 - 16 = 8

She gave away 8.

Answer: 8 candies

4 · Reviewdoes it hold up?

After the gift Jia has 16 and Minho 32: they add to 48 and stand in the ratio 1 to 2.

Another way: Following Minho instead -- he gains what Jia loses, so 24 plus the gift is 32 -- gives the same 8 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 4 easy

Jia and Minho each had $28$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $3 : 4$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 28 candies each. After one gives some to the other, their counts are in the ratio 3 to 4. We want how many were given.

Givens

Each started with 28 candies.
Afterwards the ratio is 3 to 4.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

28 + 28 = 56

Still 56 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

3 to 4 means 7 equal parts of the 56.

56 \div 7 = 8

Each part is 8 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 3 of the 7 parts.

8 \times 3 = 24

Jia has 24 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

28 - 24 = 4

She gave away 4.

Answer: 4 candies

4 · Reviewdoes it hold up?

After the gift Jia has 24 and Minho 32: they add to 56 and stand in the ratio 3 to 4.

Another way: Following Minho instead -- he gains what Jia loses, so 28 plus the gift is 32 -- gives the same 4 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 5 medium

Jia and Minho each had $30$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $2 : 3$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 30 candies each. After one gives some to the other, their counts are in the ratio 2 to 3. We want how many were given.

Givens

Each started with 30 candies.
Afterwards the ratio is 2 to 3.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

30 + 30 = 60

Still 60 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

2 to 3 means 5 equal parts of the 60.

60 \div 5 = 12

Each part is 12 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 2 of the 5 parts.

12 \times 2 = 24

Jia has 24 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

30 - 24 = 6

She gave away 6.

Answer: 6 candies

4 · Reviewdoes it hold up?

After the gift Jia has 24 and Minho 36: they add to 60 and stand in the ratio 2 to 3.

Another way: Following Minho instead -- he gains what Jia loses, so 30 plus the gift is 36 -- gives the same 6 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 6 medium

Jia and Minho each had $33$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $5 : 6$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 33 candies each. After one gives some to the other, their counts are in the ratio 5 to 6. We want how many were given.

Givens

Each started with 33 candies.
Afterwards the ratio is 5 to 6.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

33 + 33 = 66

Still 66 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

5 to 6 means 11 equal parts of the 66.

66 \div 11 = 6

Each part is 6 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 5 of the 11 parts.

6 \times 5 = 30

Jia has 30 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

33 - 30 = 3

She gave away 3.

Answer: 3 candies

4 · Reviewdoes it hold up?

After the gift Jia has 30 and Minho 36: they add to 66 and stand in the ratio 5 to 6.

Another way: Following Minho instead -- he gains what Jia loses, so 33 plus the gift is 36 -- gives the same 3 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 7 medium

Jia and Minho each had $36$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $1 : 5$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 36 candies each. After one gives some to the other, their counts are in the ratio 1 to 5. We want how many were given.

Givens

Each started with 36 candies.
Afterwards the ratio is 1 to 5.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

36 + 36 = 72

Still 72 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

1 to 5 means 6 equal parts of the 72.

72 \div 6 = 12

Each part is 12 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 1 of the 6 parts.

12 \times 1 = 12

Jia has 12 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

36 - 12 = 24

She gave away 24.

Answer: 24 candies

4 · Reviewdoes it hold up?

After the gift Jia has 12 and Minho 60: they add to 72 and stand in the ratio 1 to 5.

Another way: Following Minho instead -- he gains what Jia loses, so 36 plus the gift is 60 -- gives the same 24 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 8 medium

Jia and Minho each had $40$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $3 : 5$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 40 candies each. After one gives some to the other, their counts are in the ratio 3 to 5. We want how many were given.

Givens

Each started with 40 candies.
Afterwards the ratio is 3 to 5.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

40 + 40 = 80

Still 80 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

3 to 5 means 8 equal parts of the 80.

80 \div 8 = 10

Each part is 10 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 3 of the 8 parts.

10 \times 3 = 30

Jia has 30 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

40 - 30 = 10

She gave away 10.

Answer: 10 candies

4 · Reviewdoes it hold up?

After the gift Jia has 30 and Minho 50: they add to 80 and stand in the ratio 3 to 5.

Another way: Following Minho instead -- he gains what Jia loses, so 40 plus the gift is 50 -- gives the same 10 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 9 hard

Jia and Minho each had $42$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $5 : 7$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 42 candies each. After one gives some to the other, their counts are in the ratio 5 to 7. We want how many were given.

Givens

Each started with 42 candies.
Afterwards the ratio is 5 to 7.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

42 + 42 = 84

Still 84 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

5 to 7 means 12 equal parts of the 84.

84 \div 12 = 7

Each part is 7 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 5 of the 12 parts.

7 \times 5 = 35

Jia has 35 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

42 - 35 = 7

She gave away 7.

Answer: 7 candies

4 · Reviewdoes it hold up?

After the gift Jia has 35 and Minho 49: they add to 84 and stand in the ratio 5 to 7.

Another way: Following Minho instead -- he gains what Jia loses, so 42 plus the gift is 49 -- gives the same 7 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 10 hard

Jia and Minho each had $45$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $2 : 7$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 45 candies each. After one gives some to the other, their counts are in the ratio 2 to 7. We want how many were given.

Givens

Each started with 45 candies.
Afterwards the ratio is 2 to 7.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

45 + 45 = 90

Still 90 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

2 to 7 means 9 equal parts of the 90.

90 \div 9 = 10

Each part is 10 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 2 of the 9 parts.

10 \times 2 = 20

Jia has 20 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

45 - 20 = 25

She gave away 25.

Answer: 25 candies

4 · Reviewdoes it hold up?

After the gift Jia has 20 and Minho 70: they add to 90 and stand in the ratio 2 to 7.

Another way: Following Minho instead -- he gains what Jia loses, so 45 plus the gift is 70 -- gives the same 25 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 11 hard

Jia and Minho each had $50$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $1 : 4$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 50 candies each. After one gives some to the other, their counts are in the ratio 1 to 4. We want how many were given.

Givens

Each started with 50 candies.
Afterwards the ratio is 1 to 4.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

50 + 50 = 100

Still 100 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

1 to 4 means 5 equal parts of the 100.

100 \div 5 = 20

Each part is 20 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 1 of the 5 parts.

20 \times 1 = 20

Jia has 20 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

50 - 20 = 30

She gave away 30.

Answer: 30 candies

4 · Reviewdoes it hold up?

After the gift Jia has 20 and Minho 80: they add to 100 and stand in the ratio 1 to 4.

Another way: Following Minho instead -- he gains what Jia loses, so 50 plus the gift is 80 -- gives the same 30 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Variant 12 hard

Jia and Minho each had $60$ candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became $3 : 7$ . How many candies did Jia give away?

Your answer

Show solution

1 · Understandwhat's really being asked

Two people start with 60 candies each. After one gives some to the other, their counts are in the ratio 3 to 7. We want how many were given.

Givens

Each started with 60 candies.
Afterwards the ratio is 3 to 7.

Unknowns

How many candies Jia gave away.

Constraints

The candies only moved between the two: none were eaten or added.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #13 Convert to Algebra#7 Identify Subproblems

Both counts changed, so neither can be tracked directly. The total did not change, and that is what the new ratio divides -- work with the total and the two counts fall out.

3 · Execute4 carry out the plan

1Notice what did not change

#16 Count the Complement 6.RP.A.3

Candies moved from one person to the other, so the two together are exactly as many as before.

60 + 60 = 120

Still 120 candies.

2Cut that total in the new ratio

#7 Identify Subproblems 6.RP.A.3

3 to 7 means 10 equal parts of the 120.

120 \div 10 = 12

Each part is 12 candies.

3Find what Jia has left

#13 Convert to Algebra 6.EE.B.7

She keeps 3 of the 10 parts.

12 \times 3 = 36

Jia has 36 left.

4Compare with what she started with

#13 Convert to Algebra 6.EE.B.7

The question asks what she gave, not what she has.

60 - 36 = 24

She gave away 24.

Answer: 24 candies

4 · Reviewdoes it hold up?

After the gift Jia has 36 and Minho 84: they add to 120 and stand in the ratio 3 to 7.

Another way: Following Minho instead -- he gains what Jia loses, so 60 plus the gift is 84 -- gives the same 24 from the other side.

Standardsmin grade 6

6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for each count and then for the amount moved.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing the unchanged total in the new ratio.

💡Takeaway. When something moves between two people, look for what stayed the same. It is usually the total.

Where next?

← Back to the problem: Moving things between two people leaves the total alone