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# Algebra Percents and Simple Interest Practice Questions

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## Algebra Percents and Simple Interest Practice Questions

#### Practice 1

Answer each of the following questions.

1. What is 22 after a 50% increase?
2. What number, after a 35% increase, is 124.2?
3. What number, after a 12% increase, is 60.48?
4. What is 84 after a 75% decrease?
5. What number, after a 92% decrease, is 62?
6. What number, after a 52% decrease, is 84?

#### Practice 2

Answer each of the following questions.

1. If \$2,000 gains \$720 in interest at a rate of 4.5% per year, for how long was the principal in the bank?
2. If \$1,800 gains \$882 in interest in seven years, what was the interest rate per year?
3. If \$52 in interest is gained over three months at a rate of 5.2% per year, what was the principal?

### Solutions

#### Practice 1

1. The original value is 22 and the new value is x. Percent increase is equal to the new value minus the original value divided by the original value. Subtract 22 from x and divide by 22. Set that fraction equal to 50%, which is 0.50:

Multiply both sides of the equation by 22, and then add 22 to both sides:

x – 22 = 11

x = 33

Therefore, 22 after a 50% increase is 33.

2. The original value is unknown, so let x represent the original value. The new value is 124.2. Percent increase is equal to the new value minus the original value divided by the original value.

Subtract x from 124.2 and divide by x. Set that fraction equal to 35%, which is 0.35:

Multiply both sides of the equation by x, and then add x to both sides:

0.35x = 124.2 – x

1.35x = 124.2

Divide both sides by 1.35:

x = 92

Therefore, 92, after a 35% increase is 124.2.

3. The original value is unknown, so let x represent the original value. The new value is 60.48. Percent increase is equal to the new value minus the original value divided by the original value.

Subtract x from 60.48 and divide by x. Set that fraction equal to 12%, which is 0.12:

Multiply both sides of the equation by x, and then add x to both sides:

0.12x = 60.48 – x

1.12x = 60.48

Divide both sides by 1.12:

x = 54

Therefore, 54, after a 12% increase is 60.48.

4. The original value is 84 and the new value is x. Percent decrease is equal to the original value minus the new value divided by the original value. Subtract x from 84 and divide by 84. Set that fraction equal to 75%, which is 0.75:

Multiply both sides of the equation by 84, and then subtract 84 from both sides:

84 – x = 63

x = –21

x = 21

Therefore, 84, after a 75% decrease, is 21.

5. The original value is unknown, so let x represent the original value. The new value is 62. Percent decrease is equal to the original value minus the new value divided by the original value.

Subtract 62 from x and divide by x. Set that fraction equal to 92%, which is 0.92:

Multiply both sides of the equation by x, and then subtract x from both sides:

0.92x = x – 62

–0.08x = –62

Divide both sides by –0.08:

x = 775

Therefore, 775 after a 92% decrease is 62.

6. The original value is unknown, so let x represent the original value. The new value is 84. Percent decrease is equal to the original value minus the new value divided by the original value.

Subtract 84 from x and divide by x. Set that fraction equal to 52%, which is 0.52:

Multiply both sides of the equation by x, and then subtract x from both sides:

0.52x = x – 84

–0.48x = –84

Divide both sides by –0.48:

x = 175

Therefore, 175 after a 52% decrease is 84.

#### Practice 2

1. Because I = prt and we are looking for the time, t, we can divide both sides of the equation by pr to get t alone on the right side: =t. The rate, 4.5%, as a decimal is 0.045.

Substitute 720 for I, 2,000 for p, and 0.045 for r:

The principal was in the bank for 8 years.

2. Because I = prt and we are looking for the rate, r, we can divide both sides of the equation by pt to get r alone on the right side: =r.

Substitute 882 for I, 1,800 for p, and 7 for t:

The interest rate per year was 7%.

3. Because I = prt and we are looking for the principal, p, we can divide both sides of the equation by rt to get p alone on the right side: = p. The interest rate is given in years, but the time is given in months. There are 12 months in a year, so convert the time to years by dividing the number of months by 12: 3 ÷ 12 = 0.25. The rate, 5.2%, as a decimal is 0.052.

Substitute 52 for I, 0.052 for r, and 0.25 for t:

The principal was \$4,000.

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