AMC8 2012

AMC8 2012 · Q13

AMC8 2012 · Q13. It mainly tests Money / coins, GCD & LCM.

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?

贾马尔在学校书店买了一些每支超过一美分的铅笔，共支付 $1.43。莎罗娜买了一些同样的铅笔，支付 $1.87。莎罗娜比贾马尔多买了多少支铅笔？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (C)

正确答案：（C）

Solution

We assume that the price of the pencils remains constant. Convert $\textdollar 1.43$ and $\textdollar 1.87$ 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.

假设铅笔价格固定。将 $\textdollar 1.43$ 和 $\textdollar 1.87$ 转换为美分。由于每支超过一美分，单支价格（美分）为 143 和 187 的最大公因数，为 $11$。因此，贾马尔买 $\frac{143}{11} \implies 13$ 支，莎罗娜买 $\frac{187}{11} \implies 17$ 支。莎罗娜多买 $17-13 = \boxed{\textbf{(C)}\ 4}$ 支。

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