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A bookstore ordered 10 boxes of hardcover books and some boxes of paperback books. Hardcovers cost twice as much per box as paperbacks. Due to an order error, the quantities were swapped, increasing the bill by 20%. What is the ratio of hardcover to paperback boxes originally?

1. 4:7
2. 1:3
3. 2:3
4. 3:2

Correct answer: 4:7

Solution

Let the number of paperback boxes be $x$ and hardcover boxes be 10. If paperback costs 1 unit per box, hardcover costs 2 units. Original bill = $10\cdot2 + x\cdot1 = 20+x$. After swapping, bill = $x\cdot2 + 10\cdot1 = 2x+10$. Since the bill increases by 20%, $2x+10 = 1.2(20+x)$, giving $x=17.5$, so the ratio is $10:17.5 = 4:7$.

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