Question

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

$2$

$3$

$4$

$5$

$6$

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Written solution:

Let $c$ be the price of one pencil in cents. Then $c$ divides both $143$ and $187$ , and $c\gt1$ .

Since $143=11\cdot13$ and $187=11\cdot17$ , the greatest common divisor is $11$ . Thus each pencil costs $11$ cents.

Sharona paid $187-143=44$ cents more, so she bought $44/11=4$ more pencils. Thus, the answer is C .

2012 AMC 8 Problem 13

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Problem 13 in Other Years