HMMT 二月 2000 · GEN 赛 · 第 10 题
HMMT February 2000 — GEN Round — Problem 10
题目详情
英文原题
- 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 outthe neigh b or's dog. Normal fen ep osts ost $2 each while strong ones ost $3 each. Ifhe needs one fen ep ost for ev ery 2 feet and has $70 to sp end on the fen ep osts, what isthe largest number of strong fen ep osts he an buy?
a + b
解析
英文解析
- On the 12 fo ot sides, he needs 7 p osts, and on the 20 fo ot sides, he needs 9 p osts, so heneeds 7 + 9 + 7 + 9 = 32 total p osts. Let x be the number of normal fen ep osts and ybe the number of strong fen ep osts, so x + y = 32. T o sp end $70, we have the equation
2 x + 3 y = 70. Substituting, we nd that 2(32 y ) + 3 y = 70, so 64 2 y + 3 y = 70, and
64 + y = 70, so y = 6 .
3+ n 3