ACT Math - How to find the percent of increase

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%

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.

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 :

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

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.

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

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

$x \cdot 1.2 = 1.2x$ 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 .

What is the percent increase from to ?

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.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{.077-.043}{.043} = 79.0697 % \approx 79.070 %$

A university has students currently enrolled in its freshman class. Last year, there were only freshman enrolled at the school. By what percentage did the number of students in the freshman class increase?

Explanation

To find the percentage increase, use the following formula:

Increased # of students this year / # of students last year

If there were students last year, and this year there are , the number of students increased by . Then, knowing this, you can find what percentage of the original number () represents.

Therefore:

$\frac{570-500}{500} = \frac{70}{500}=\frac{14}{100}=0.14$

The number of students increased by .

Truck A has a length of 8'3" (8 ft. and 3 inches). Truck B has a length of 14'5".

What is the percentage increase in length going from Truck A to Truck B?

35.42

74.74

79.11

66.53

Explanation

Find a common unit—in this case it is inches. The increase is from 99” to 173”. To find the percentage increase we find the difference and then divide by the length of Truck A.

$\frac{173-99}{99}=\frac{74}{99}\approx 0.7474$

or 74.74%

Ben and Sam have a furniture design business. The first year they earn $10,000 in profits. The second year they earn $12,000 in profits. What is the percentage increase in profit between year one and two?

20%

25%

12%

10%

Explanation

Percentage Increase = (Year Two Profit – Year One Profit) / Year One Profit

= ($12,000 - $10,000) / $10,000 = $2000 / $10,000 = .2 = 20%

A fundraiser for a local charity raised $28,000 in donations last year. The fundraiser’s goal for this year is to exceed last year’s donations by 15%. So far, they have raised $31,000. How much more money must the fundraiser raise to reach their goal?

$1200

$1500

$3200

$4200

$5500

Explanation

First, let's calculate the value of this year's expected goal. Start by calculating 15 percent of last year's goal. Do this by converting 15 percent to a decimal by moving the decimal point two spaces to the left, and then multiplying this number by last year's goal.

$15%\rightarrow 0.15$