← Read a ratio as equal parts and a difference tells you what one is worth · Proportion and Proportional Division

Read a ratio as equal parts and a difference tells you what one is worth · 12 practice problems

6.RP.A.36.EE.B.7

Generated variants — 12

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

Variant 1 easy answer: 2250 won

The ratio of Jua's allowance to Eunwoo's is 7:97 : 9, and Eunwoo received 500500 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 7 to 9, and the second is 500 won more. We want the second one.

Givens
  • The ratio is 7 to 9.
  • The second allowance is 500 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 7 parts and Eunwoo 9, all the same size.
7:97 : 9
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
9−7=29 - 7 = 2
2 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 2 parts come to 500 won.
500÷2=250500 \div 2 = 250
A part is 250 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 9 of them.
250×9=2250250 \times 9 = 2250
Eunwoo received 2250 won.
Answer: 2250 won
4 · Reviewdoes it hold up?

Jua has 1750 won and Eunwoo 2250: they differ by 500 won and stand in the ratio 7 to 9.

Another way: Writing the two as 7 times a number and 9 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 2 easy answer: 5400 won

The ratio of Jua's allowance to Eunwoo's is 8:98 : 9, and Eunwoo received 600600 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 8 to 9, and the second is 600 won more. We want the second one.

Givens
  • The ratio is 8 to 9.
  • The second allowance is 600 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 8 parts and Eunwoo 9, all the same size.
8:98 : 9
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
9−8=19 - 8 = 1
1 part of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 1 part come to 600 won.
600÷1=600600 \div 1 = 600
A part is 600 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 9 of them.
600×9=5400600 \times 9 = 5400
Eunwoo received 5400 won.
Answer: 5400 won
4 · Reviewdoes it hold up?

Jua has 4800 won and Eunwoo 5400: they differ by 600 won and stand in the ratio 8 to 9.

Another way: Writing the two as 8 times a number and 9 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 3 easy answer: 2000 won

The ratio of Jua's allowance to Eunwoo's is 3:53 : 5, and Eunwoo received 800800 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 3 to 5, and the second is 800 won more. We want the second one.

Givens
  • The ratio is 3 to 5.
  • The second allowance is 800 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 3 parts and Eunwoo 5, all the same size.
3:53 : 5
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
5−3=25 - 3 = 2
2 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 2 parts come to 800 won.
800÷2=400800 \div 2 = 400
A part is 400 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 5 of them.
400×5=2000400 \times 5 = 2000
Eunwoo received 2000 won.
Answer: 2000 won
4 · Reviewdoes it hold up?

Jua has 1200 won and Eunwoo 2000: they differ by 800 won and stand in the ratio 3 to 5.

Another way: Writing the two as 3 times a number and 5 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 4 easy answer: 2400 won

The ratio of Jua's allowance to Eunwoo's is 5:85 : 8, and Eunwoo received 900900 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 5 to 8, and the second is 900 won more. We want the second one.

Givens
  • The ratio is 5 to 8.
  • The second allowance is 900 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 5 parts and Eunwoo 8, all the same size.
5:85 : 8
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
8−5=38 - 5 = 3
3 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 3 parts come to 900 won.
900÷3=300900 \div 3 = 300
A part is 300 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 8 of them.
300×8=2400300 \times 8 = 2400
Eunwoo received 2400 won.
Answer: 2400 won
4 · Reviewdoes it hold up?

Jua has 1500 won and Eunwoo 2400: they differ by 900 won and stand in the ratio 5 to 8.

Another way: Writing the two as 5 times a number and 8 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 5 medium answer: 3250 won

The ratio of Jua's allowance to Eunwoo's is 9:139 : 13, and Eunwoo received 10001000 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 9 to 13, and the second is 1000 won more. We want the second one.

Givens
  • The ratio is 9 to 13.
  • The second allowance is 1000 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 9 parts and Eunwoo 13, all the same size.
9:139 : 13
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
13−9=413 - 9 = 4
4 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 4 parts come to 1000 won.
1000÷4=2501000 \div 4 = 250
A part is 250 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 13 of them.
250×13=3250250 \times 13 = 3250
Eunwoo received 3250 won.
Answer: 3250 won
4 · Reviewdoes it hold up?

Jua has 2250 won and Eunwoo 3250: they differ by 1000 won and stand in the ratio 9 to 13.

Another way: Writing the two as 9 times a number and 13 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 6 medium answer: 2800 won

The ratio of Jua's allowance to Eunwoo's is 4:74 : 7, and Eunwoo received 12001200 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 4 to 7, and the second is 1200 won more. We want the second one.

Givens
  • The ratio is 4 to 7.
  • The second allowance is 1200 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 4 parts and Eunwoo 7, all the same size.
4:74 : 7
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
7−4=37 - 4 = 3
3 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 3 parts come to 1200 won.
1200÷3=4001200 \div 3 = 400
A part is 400 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 7 of them.
400×7=2800400 \times 7 = 2800
Eunwoo received 2800 won.
Answer: 2800 won
4 · Reviewdoes it hold up?

Jua has 1600 won and Eunwoo 2800: they differ by 1200 won and stand in the ratio 4 to 7.

Another way: Writing the two as 4 times a number and 7 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 7 medium answer: 4500 won

The ratio of Jua's allowance to Eunwoo's is 2:32 : 3, and Eunwoo received 15001500 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 2 to 3, and the second is 1500 won more. We want the second one.

Givens
  • The ratio is 2 to 3.
  • The second allowance is 1500 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 2 parts and Eunwoo 3, all the same size.
2:32 : 3
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
3−2=13 - 2 = 1
1 part of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 1 part come to 1500 won.
1500÷1=15001500 \div 1 = 1500
A part is 1500 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 3 of them.
1500×3=45001500 \times 3 = 4500
Eunwoo received 4500 won.
Answer: 4500 won
4 · Reviewdoes it hold up?

Jua has 3000 won and Eunwoo 4500: they differ by 1500 won and stand in the ratio 2 to 3.

Another way: Writing the two as 2 times a number and 3 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 8 medium answer: 3600 won

The ratio of Jua's allowance to Eunwoo's is 5:95 : 9, and Eunwoo received 16001600 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 5 to 9, and the second is 1600 won more. We want the second one.

Givens
  • The ratio is 5 to 9.
  • The second allowance is 1600 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 5 parts and Eunwoo 9, all the same size.
5:95 : 9
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
9−5=49 - 5 = 4
4 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 4 parts come to 1600 won.
1600÷4=4001600 \div 4 = 400
A part is 400 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 9 of them.
400×9=3600400 \times 9 = 3600
Eunwoo received 3600 won.
Answer: 3600 won
4 · Reviewdoes it hold up?

Jua has 2000 won and Eunwoo 3600: they differ by 1600 won and stand in the ratio 5 to 9.

Another way: Writing the two as 5 times a number and 9 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 9 hard answer: 4400 won

The ratio of Jua's allowance to Eunwoo's is 6:116 : 11, and Eunwoo received 20002000 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 6 to 11, and the second is 2000 won more. We want the second one.

Givens
  • The ratio is 6 to 11.
  • The second allowance is 2000 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 6 parts and Eunwoo 11, all the same size.
6:116 : 11
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
11−6=511 - 6 = 5
5 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 5 parts come to 2000 won.
2000÷5=4002000 \div 5 = 400
A part is 400 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 11 of them.
400×11=4400400 \times 11 = 4400
Eunwoo received 4400 won.
Answer: 4400 won
4 · Reviewdoes it hold up?

Jua has 2400 won and Eunwoo 4400: they differ by 2000 won and stand in the ratio 6 to 11.

Another way: Writing the two as 6 times a number and 11 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 10 hard answer: 4200 won

The ratio of Jua's allowance to Eunwoo's is 3:73 : 7, and Eunwoo received 24002400 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 3 to 7, and the second is 2400 won more. We want the second one.

Givens
  • The ratio is 3 to 7.
  • The second allowance is 2400 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 3 parts and Eunwoo 7, all the same size.
3:73 : 7
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
7−3=47 - 3 = 4
4 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 4 parts come to 2400 won.
2400÷4=6002400 \div 4 = 600
A part is 600 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 7 of them.
600×7=4200600 \times 7 = 4200
Eunwoo received 4200 won.
Answer: 4200 won
4 · Reviewdoes it hold up?

Jua has 1800 won and Eunwoo 4200: they differ by 2400 won and stand in the ratio 3 to 7.

Another way: Writing the two as 3 times a number and 7 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 11 hard answer: 6000 won

The ratio of Jua's allowance to Eunwoo's is 7:127 : 12, and Eunwoo received 25002500 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 7 to 12, and the second is 2500 won more. We want the second one.

Givens
  • The ratio is 7 to 12.
  • The second allowance is 2500 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 7 parts and Eunwoo 12, all the same size.
7:127 : 12
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
12−7=512 - 7 = 5
5 parts of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 5 parts come to 2500 won.
2500÷5=5002500 \div 5 = 500
A part is 500 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 12 of them.
500×12=6000500 \times 12 = 6000
Eunwoo received 6000 won.
Answer: 6000 won
4 · Reviewdoes it hold up?

Jua has 3500 won and Eunwoo 6000: they differ by 2500 won and stand in the ratio 7 to 12.

Another way: Writing the two as 7 times a number and 12 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.
Variant 12 hard answer: 15000 won

The ratio of Jua's allowance to Eunwoo's is 4:54 : 5, and Eunwoo received 30003000 won more than Jua. How much did Eunwoo receive?

Show solution
1 · Understandwhat's really being asked

Two allowances are in the ratio 4 to 5, and the second is 3000 won more. We want the second one.

Givens
  • The ratio is 4 to 5.
  • The second allowance is 3000 won more than the first.
Unknowns
  • Eunwoo's allowance.
Constraints
  • Neither amount is given directly.
2 · Planchoose the strategy

#10 Create a Physical Representation · also uses: #13 Convert to Algebra#7 Identify Subproblems

Read the ratio as equal parts rather than as two numbers: then the difference between the two people is a whole number of parts, and one division says what a part is worth.

3 · Execute4 carry out the plan

1Read the ratio as parts

#10 Create a Physical Representation 6.RP.A.3
Jua has 4 parts and Eunwoo 5, all the same size.
4:54 : 5
Equal parts, different counts.

2Count the parts in the difference

#7 Identify Subproblems 6.RP.A.3
Eunwoo's extra is the gap between the two counts.
5−4=15 - 4 = 1
1 part of difference.

3Find one part

#13 Convert to Algebra 6.EE.B.7
Those 1 part come to 3000 won.
3000÷1=30003000 \div 1 = 3000
A part is 3000 won.

4Give Eunwoo his parts

#13 Convert to Algebra 6.EE.B.7
He has 5 of them.
3000×5=150003000 \times 5 = 15000
Eunwoo received 15000 won.
Answer: 15000 won
4 · Reviewdoes it hold up?

Jua has 12000 won and Eunwoo 15000: they differ by 3000 won and stand in the ratio 4 to 5.

Another way: Writing the two as 4 times a number and 5 times the same number and subtracting gives the same equation with the parts left unnamed.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the ratio as equal parts and locating the difference.
  • 6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for one part and scaling it back up.
💡Takeaway. A ratio is a count of equal parts. Any real difference tells you what one part is worth.