ACT Math - How to find amount of profit

Manufacturing a particular product produces a profit of for each unit produced. If the cost to produce a unit is , what is the profit percentage on each unit? Do not round until the final answer.

Explanation

Calculating a percentage profit is the same as calculating a percent change. 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.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{3.05-2.55}{2.55} = 19.607 % \approx 19.6 %$

A bakery sells cupcakes for per dozen. If it costs to make each dozen, how much profit would the bakery earn from selling dozen cupcakes?

Explanation

The profit that is made is the difference between the amount earned and the amount spent. In this instance, it costs to make a dozen cupcakes, but the bakery charges per dozen.

To find the profit for one dozen cupcakes:

To find the profit for ten dozen cupcakes:

$$7.50\cdot 10 = $75.00$

It costs a retail store to purchase a bow tie. If this store sells the bow tie for , what is its profit percentage? Round to the nearest hundredth.

Explanation

The profit percentage is really just a matter of percent change. We are changing from to . This is easily computed as:

$\frac{15.5-3.25}{3.25}=3.76923076923077...$

This is the same as !

In business, profit is defined as revenue minus expenses. A profit is often expressed as a percentage of total revenue.

A company posts a profit for the first quarter of the new year, pleasing investors. If the total profits for the quarter were what were the expenses for the company in that quarter? Round to the nearest dollar.

Explanation

If a profit of represents , then we can calculate revenue as:

$x = \frac{33,500,000}{0.28} \approx 119,642,857$

Now, subtract the profit from the total revenue to calculate expenses:

$e \approx 119,642,857 - 33,500,000 \approx 86,142,857$

Thus, the quarterly expenses were .

A set of cards were purchased for . If the store earned profit on the sale, what was the original price of the cards? Round to the nearest hundredth.

Explanation

This question is really asking a hidden percentage change question. It really means, "The price changed from to , signalling a change." Thus, you can set up an equation like this:

$\frac{45-x}{x}=0.35$

Solving for , you get:

Jenny has two jobs. The first is an office job salaried at $52,000 per year, so she makes the same amount of money every week, no matter how many hours she works. The second is a bartending job. She works 6 hours a night, 2 nights a week. She earns $3.50 per hour plus tips. If she earned $450 in tips this week, what is the total amount of money she made this week?

$1,492

$1,021

$1,000

$1,450

$1,480

Explanation

Salaried job:

$52,000 / year

1 year = 52 weeks

Therefore: $52,000 / 52 weeks = $1,000.00 per week

Bartending job:

6 hours x $3.50 per hour x 2 nights per week = $42.00

Total Earned = Salaried + Bartending + Tips

= $1,000.00 + $42.00 + $450 = $1,492

Sam was helping his school raise funds to buy books for the library. He bought small paper pads for $0.75 and sold them for $2.00. What was the percent mark-up, rounded to the nearest whole number?

167%

66%

150%

75%

None of the answers are correct

Explanation

$ Mark-Up = $ New Price – $ Original Price

% Mark-Up = $ Mark-Up ÷ $ Original Price

% Mark-Up = (2.00 – 0.75) ÷ 0.75 = 1.67 or 167 %

The profit on a particular product per unit is measured as a percentage of the cost to produce that unit. If units are produced at a total cost of , and sell for a total of , what was the profit per unit, as a percentage?

Explanation

Remember, percentage profit is a ratio between two numbers. The ratio stays the same whether the numbers reflect hundreds of units sold or just one unit (unless otherwise told). So to find our answer, we only need to calculate the overall profit percentage.

$T_{change} = 100 \cdot \frac{T_2-T_1}{T_1} = 100 \cdot \frac{27000-12000}{12000} = 125 %$

A cassette tape sells for , and the producer receives a cut of of each sale. If the producer spends of the sale price in manufacturing and producing expenses, how much money is made on the sale of each tape?