Competition problem — Number theory

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Number theory Difficulty 3.4 AMC 10/12 Find the answer

Jamar bought some pencils costing more than a penny each at the school bookstore and paid $\text{1.43}$ . Sharona bought some of the same pencils and paid $\text{1.87}$ . How many more pencils did Sharona buy than Jamar?

Pick one

Solution

We assume that the price of the pencils remains constant. Convert $\text{1.43}$ and $\text{1.87}$ to cents. Since the price of the pencils is more than one penny, we can find the price of one pencil (in cents) by taking the greatest common divisor of $143$ and $187$ , which is $11$ . Therefore, Jamar bought $\frac{143}{11} \implies 13$ pencils and Sharona bought $\frac{187}{11} \implies 17$ pencils. Thus, Sharona bought $17-13 = \boxed{\textbf{(C)}\ 4}$ more pencils than Jamar.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.