# Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 1 • Question 23

Molly sold two books for a total of £180. She had bought both books at the same price. She made a 25% loss on the cost of one of them. And she made a 75% profit on the cost of the other. Work out the percentage profit on the total cost of the books.

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### Video Transcript

Molly sold two books for a total of 180 pounds. She had bought both books at the same price. She made a 25 percent loss on the cost of one of them. And she made a 75 percent profit on the cost of the other. Work out the percentage profit on the total cost of the books.

To solve this problem, we’ll need to set up an equation. We’ll let 𝑃 be the original price of a one book. Molly made a 25 percent loss on the first book. That means she earned back 75 percent of the original price. We can write that as 0.75 times 𝑃. She sold the second book at a 75 percent profit which means she made back everything she invested: one whole plus a 75 percent profit. She made 1.75 of the original price: 1.75 times 𝑃.

If we add what she made from the first book and the second book, it equals 180 pounds because we know she sold both books together for 180 pounds. Combining 0.75 and 1.75 equals 2.5𝑃 which equals 180 pounds. If we divide both sides of the equation by 2.5, we’ll find the original price of one book equals 72 pounds. But how does that help us find the percentage profit?

Molly’s percentage profit equals the money she made selling her books minus the cost of her books divided by the cost of books. We know that Molly sold her books for 180 pounds. That’s the money she made. How would we find the cost of the books?

She bought both books at the same price and that price was 72 pounds: two times 72 pounds. The cost of both books is 144 pounds. And that means the denominator is also 144 pounds. 180 minus 144 equals 36. 36 divided by 144 equals 0.25.

Notice that we want a percentage profit and that currently we have a decimal. In order to calculate the percent, you need to take your decimal value and multiply it by 100. 0.25 times 100 equals 25.

The percentage profit Molly had was 25.