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?

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1. Let paperback price be $P$. Then hardcover price is $2P$.  Let paperback boxes be $x$.

2. Original cost = $10\cdot2P + x\cdot P = (20+x)P$. Swapped cost = $10P + x\cdot2P = (10+2x)P$.

3. Swap raises bill by 20%: $10+2x=1.2(20+x)$. So $10+2x=24+1.2x$, giving $0.8x=14$ and $x=17.5$.

4. Ratio hardcover:paperback = $10:17.5 = 20:35 = 4:7$. So answer (a).

FINAL_ANSWER: a

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