GMAT
题目
Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?
解析
设铅笔数量分别为\( J \)、\( K \)、\( L \)。
我们需要求解这个整数方程组（其中\( J,K,L≥0 \)）：
\( 5J + 10K + 25L = 340 \)
\( J + K + L = 32 \)
\( K = 2L \)
代入\( K = 2L \)化简：
\( J + 4L + 5L = 68 \)
\( J + 2L + L = 32 \)
进一步整理为：
\( J + 9L = 68 \)
\( J + 3L = 32 \)
两式相减得：
\( 6L = 68 - 32 = 36 \)
\( L = 6 \)
代入求\( J \)：
\( J = 32 - 3L = 32 - 18 = 14 \)
答案是C
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