← Interest is a rate on the principal, and the principal comes back too · Ratio, Rate and Percent

Interest is a rate on the principal, and the principal comes back too · 12 practice problems

7.RP.A.36.RP.A.3

Generated variants — 12

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

Variant 1 easy answer: 303,000 won

Depositing 250,000250{,}000 won in a bank for one year earns 25002500 won in interest. If Sua deposits 300,000300{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

250,000 won earns 2,500 won of interest in a year. Sua puts in 300,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 250,000 won earns 2,500 won in one year.
  • Sua deposits 300,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
2,500÷250,000=0.01=1%2,500 \div 250{,}000 = 0.01 = 1\%
The bank pays 1 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 300,000 won.
300,000×0.01=3,000300{,}000 \times 0.01 = 3{,}000
She earns 3,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
300,000+3,000=303,000300{,}000 + 3{,}000 = 303{,}000
303,000 won in total.
Answer: 303,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.01 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 300,000:250,000300{,}000 : 250{,}000 skips the percentage and lands on the same 3,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 2 easy answer: 360,500 won

Depositing 100,000100{,}000 won in a bank for one year earns 30003000 won in interest. If Sua deposits 350,000350{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

100,000 won earns 3,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 100,000 won earns 3,000 won in one year.
  • Sua deposits 350,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
3,000÷100,000=0.03=3%3,000 \div 100{,}000 = 0.03 = 3\%
The bank pays 3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 350,000 won.
350,000×0.03=10,500350{,}000 \times 0.03 = 10{,}500
She earns 10,500 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
350,000+10,500=360,500350{,}000 + 10{,}500 = 360{,}500
360,500 won in total.
Answer: 360,500 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.03 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 350,000:100,000350{,}000 : 100{,}000 skips the percentage and lands on the same 10,500 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 3 easy answer: 615,000 won

Depositing 150,000150{,}000 won in a bank for one year earns 37503750 won in interest. If Sua deposits 600,000600{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

150,000 won earns 3,750 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 150,000 won earns 3,750 won in one year.
  • Sua deposits 600,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
3,750÷150,000=0.025=2.5%3,750 \div 150{,}000 = 0.025 = 2.5\%
The bank pays 2.5 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 600,000 won.
600,000×0.025=15,000600{,}000 \times 0.025 = 15{,}000
She earns 15,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
600,000+15,000=615,000600{,}000 + 15{,}000 = 615{,}000
615,000 won in total.
Answer: 615,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.025 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 600,000:150,000600{,}000 : 150{,}000 skips the percentage and lands on the same 15,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 4 easy answer: 867,000 won

Depositing 350,000350{,}000 won in a bank for one year earns 70007000 won in interest. If Sua deposits 850,000850{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

350,000 won earns 7,000 won of interest in a year. Sua puts in 850,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 350,000 won earns 7,000 won in one year.
  • Sua deposits 850,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
7,000÷350,000=0.02=2%7,000 \div 350{,}000 = 0.02 = 2\%
The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 850,000 won.
850,000×0.02=17,000850{,}000 \times 0.02 = 17{,}000
She earns 17,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
850,000+17,000=867,000850{,}000 + 17{,}000 = 867{,}000
867,000 won in total.
Answer: 867,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 850,000:350,000850{,}000 : 350{,}000 skips the percentage and lands on the same 17,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 5 medium answer: 355,250 won

Depositing 600,000600{,}000 won in a bank for one year earns 90009000 won in interest. If Sua deposits 350,000350{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

600,000 won earns 9,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 600,000 won earns 9,000 won in one year.
  • Sua deposits 350,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
9,000÷600,000=0.015=1.5%9,000 \div 600{,}000 = 0.015 = 1.5\%
The bank pays 1.5 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 350,000 won.
350,000×0.015=5,250350{,}000 \times 0.015 = 5{,}250
She earns 5,250 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
350,000+5,250=355,250350{,}000 + 5{,}250 = 355{,}250
355,250 won in total.
Answer: 355,250 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.015 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 350,000:600,000350{,}000 : 600{,}000 skips the percentage and lands on the same 5,250 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 6 medium answer: 613,800 won

Depositing 400,000400{,}000 won in a bank for one year earns 92009200 won in interest. If Sua deposits 600,000600{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

400,000 won earns 9,200 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 400,000 won earns 9,200 won in one year.
  • Sua deposits 600,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
9,200÷400,000=0.023=2.3%9,200 \div 400{,}000 = 0.023 = 2.3\%
The bank pays 2.3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 600,000 won.
600,000×0.023=13,800600{,}000 \times 0.023 = 13{,}800
She earns 13,800 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
600,000+13,800=613,800600{,}000 + 13{,}800 = 613{,}800
613,800 won in total.
Answer: 613,800 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.023 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 600,000:400,000600{,}000 : 400{,}000 skips the percentage and lands on the same 13,800 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 7 medium answer: 918,000 won

Depositing 500,000500{,}000 won in a bank for one year earns 1000010000 won in interest. If Sua deposits 900,000900{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

500,000 won earns 10,000 won of interest in a year. Sua puts in 900,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 500,000 won earns 10,000 won in one year.
  • Sua deposits 900,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
10,000÷500,000=0.02=2%10,000 \div 500{,}000 = 0.02 = 2\%
The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 900,000 won.
900,000×0.02=18,000900{,}000 \times 0.02 = 18{,}000
She earns 18,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
900,000+18,000=918,000900{,}000 + 18{,}000 = 918{,}000
918,000 won in total.
Answer: 918,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 900,000:500,000900{,}000 : 500{,}000 skips the percentage and lands on the same 18,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 8 medium answer: 818,400 won

Depositing 450,000450{,}000 won in a bank for one year earns 1035010350 won in interest. If Sua deposits 800,000800{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

450,000 won earns 10,350 won of interest in a year. Sua puts in 800,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 450,000 won earns 10,350 won in one year.
  • Sua deposits 800,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
10,350÷450,000=0.023=2.3%10,350 \div 450{,}000 = 0.023 = 2.3\%
The bank pays 2.3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 800,000 won.
800,000×0.023=18,400800{,}000 \times 0.023 = 18{,}400
She earns 18,400 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
800,000+18,400=818,400800{,}000 + 18{,}400 = 818{,}400
818,400 won in total.
Answer: 818,400 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.023 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 800,000:450,000800{,}000 : 450{,}000 skips the percentage and lands on the same 18,400 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 9 hard answer: 102,000 won

Depositing 750,000750{,}000 won in a bank for one year earns 1500015000 won in interest. If Sua deposits 100,000100{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

750,000 won earns 15,000 won of interest in a year. Sua puts in 100,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 750,000 won earns 15,000 won in one year.
  • Sua deposits 100,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
15,000÷750,000=0.02=2%15,000 \div 750{,}000 = 0.02 = 2\%
The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 100,000 won.
100,000×0.02=2,000100{,}000 \times 0.02 = 2{,}000
She earns 2,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
100,000+2,000=102,000100{,}000 + 2{,}000 = 102{,}000
102,000 won in total.
Answer: 102,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 100,000:750,000100{,}000 : 750{,}000 skips the percentage and lands on the same 2,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 10 hard answer: 357,000 won

Depositing 900,000900{,}000 won in a bank for one year earns 1800018000 won in interest. If Sua deposits 350,000350{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

900,000 won earns 18,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 900,000 won earns 18,000 won in one year.
  • Sua deposits 350,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
18,000÷900,000=0.02=2%18,000 \div 900{,}000 = 0.02 = 2\%
The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 350,000 won.
350,000×0.02=7,000350{,}000 \times 0.02 = 7{,}000
She earns 7,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
350,000+7,000=357,000350{,}000 + 7{,}000 = 357{,}000
357,000 won in total.
Answer: 357,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 350,000:900,000350{,}000 : 900{,}000 skips the percentage and lands on the same 7,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 11 hard answer: 669,500 won

Depositing 900,000900{,}000 won in a bank for one year earns 2700027000 won in interest. If Sua deposits 650,000650{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

900,000 won earns 27,000 won of interest in a year. Sua puts in 650,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 900,000 won earns 27,000 won in one year.
  • Sua deposits 650,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
27,000÷900,000=0.03=3%27,000 \div 900{,}000 = 0.03 = 3\%
The bank pays 3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 650,000 won.
650,000×0.03=19,500650{,}000 \times 0.03 = 19{,}500
She earns 19,500 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
650,000+19,500=669,500650{,}000 + 19{,}500 = 669{,}500
669,500 won in total.
Answer: 669,500 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.03 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 650,000:900,000650{,}000 : 900{,}000 skips the percentage and lands on the same 19,500 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.
Variant 12 hard answer: 624,000 won

Depositing 700,000700{,}000 won in a bank for one year earns 2800028000 won in interest. If Sua deposits 600,000600{,}000 won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Show solution
1 · Understandwhat's really being asked

700,000 won earns 28,000 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens
  • 700,000 won earns 28,000 won in one year.
  • Sua deposits 600,000 won.
  • The rate is the same for both deposits.
Unknowns
  • The total Sua can withdraw after one year.
Constraints
  • Interest is proportional to the amount deposited.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3
Divide the interest by the deposit it came from.
28,000÷700,000=0.04=4%28,000 \div 700{,}000 = 0.04 = 4\%
The bank pays 4 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3
The same rate on 600,000 won.
600,000×0.04=24,000600{,}000 \times 0.04 = 24{,}000
She earns 24,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3
Withdrawing in all means her own money plus what it earned.
600,000+24,000=624,000600{,}000 + 24{,}000 = 624{,}000
624,000 won in total.
Answer: 624,000 won
4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.04 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio 600,000:700,000600{,}000 : 700{,}000 skips the percentage and lands on the same 24,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7
  • 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.
💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.