HMMT 二月 2000 · GEN 赛 · 第 10 题
HMMT February 2000 — GEN Round — Problem 10
题目详情
- Bob has a 12 fo ot b y 20 fo ot garden. He w an ts to put fen ing around it to k eep out the neigh b or's dog. Normal fen ep osts ost 3 ea h. If he needs one fen ep ost for ev ery 2 feet and has $70 to sp end on the fen ep osts, what is the largest n um b er of strong fen ep osts he an buy? a + b
解析
- On the 12 fo ot sides, he needs 7 p osts, and on the 20 fo ot sides, he needs 9 p osts, so he needs 7 + 9 + 7 + 9 = 32 total p osts. Let x b e the n um b er of normal fen ep osts and y b e the n um b er of strong fen ep osts, so x + y = 32. T o sp end $70, w e ha v e the equation 2 x + 3 y = 70. Substituting, w e nd that 2(32 y ) + 3 y = 70, so 64 2 y + 3 y = 70, and 64 + y = 70, so y = 6 . 3 3+ n