ACT Math - Percent of Change

1

Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.

34.3%

33.4%

22.9%

25.7%

40.0%

Explanation

Pay = Hours worked x Rate per hour

Retail job = 20 x $8.50 = $170.00

Office job = 15 x $12.00 = $180.00

Current weekly pay = $170.00 + $180.00 = $350.00

Additional Office job hours = 10 x $12.00 = $120.00

Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%

2

On a given day, the temperature ranges from a low of $15 ^{\circ} C$ to a high of $22^{\circ} C$ . What is the percent increase of temperature from the day's low to high temperature? Round to the nearest integer.

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{22-15}{15} = 46.66 % \approx 47 %$

Thus, there was a increase in temperature that day.

3

Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.

34.3%

33.4%

22.9%

25.7%

40.0%

Explanation

Pay = Hours worked x Rate per hour

Retail job = 20 x $8.50 = $170.00

Office job = 15 x $12.00 = $180.00

Current weekly pay = $170.00 + $180.00 = $350.00

Additional Office job hours = 10 x $12.00 = $120.00

Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%

4

On a given day, the temperature ranges from a low of $15 ^{\circ} C$ to a high of $22^{\circ} C$ . What is the percent increase of temperature from the day's low to high temperature? Round to the nearest integer.

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{22-15}{15} = 46.66 % \approx 47 %$

Thus, there was a increase in temperature that day.

5

What is the percent increase from of a number to of that same number?

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, don't forget :

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{.40x-.18x}{.18x} = 122.22 % \approx 122 %$

6

What is the percent increase from of a number to of that same number?

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, don't forget :

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{.40x-.18x}{.18x} = 122.22 % \approx 122 %$

7

The price of a particular metal raises from $\frac{$ 5.52}{oz}$ to $\frac{$ 6.17}{oz}$ . What percent increase did the price see?

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{6.17-5.52}{5.52} = 11.7 % \approx 12 %$

8

The price of a particular metal raises from $\frac{$ 5.52}{oz}$ to $\frac{$ 6.17}{oz}$ . What percent increase did the price see?

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{6.17-5.52}{5.52} = 11.7 % \approx 12 %$

9

A particular stock gains on its price on Tuesday. On Wednesday, it loses of its new price. On Thursday, it gains on Wednesday's price. What is the percent increase at the close of business Thursday, compared to the opening price on Tuesday? Do not round until the final answer.

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, to keep our amount constantly compared to Tuesday, set Tuesday's price as a variable.

$x \cdot 1.2 = 1.2x$ On Tuesday, gain 20 percent.

$1.2x \cdot .88 = 1.056x$ On Wednesday, lose 12 percent (thus, multiply by 88 percent).

$1.056x\cdot 1.04 = 1.09824x \approx 1.10x$ On Thursday, gain 4 percent.

Thus, our final gain relative to Tuesday is .

10

A particular stock gains on its price on Tuesday. On Wednesday, it loses of its new price. On Thursday, it gains on Wednesday's price. What is the percent increase at the close of business Thursday, compared to the opening price on Tuesday? Do not round until the final answer.

Explanation

To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, to keep our amount constantly compared to Tuesday, set Tuesday's price as a variable.

$x \cdot 1.2 = 1.2x$ On Tuesday, gain 20 percent.

$1.2x \cdot .88 = 1.056x$ On Wednesday, lose 12 percent (thus, multiply by 88 percent).

$1.056x\cdot 1.04 = 1.09824x \approx 1.10x$ On Thursday, gain 4 percent.

Thus, our final gain relative to Tuesday is .

Percent of Change

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