HMMT 二月 1998 · 代数 · 第 1 题

HMMT February 1998 — Algebra — Problem 1

The cost of 3 hamburgers, 5 milk shakes, and 1 order of fries at a certain fast food restaurant is $23.50. At the same restaurant, the cost of 5 hamburgers, 9 milk shakes, and 1 order of fries is $39.50. What is the cost of 2 hamburgers, 2 milk shakes and 2 orders of fries at this restaurant?

解析

Problem: The cost of 3 hamburgers, 5 milk shakes, and 1 order of fries at a certain fast food restaurant is $23.50. At the same restaurant, the cost of 5 hamburgers, 9 milk shakes, and 1 order of fries is$ 39.50. What is the cost of 2 hamburgers, 2 milk shakes ,and 2 orders of fries at this restaurant? Solution: Let H = hamburger, M = milk shake, and F = order of fries. Then 3 H + 5 M + F = $23 . 50. Multiplying the equation by 2 yields 6 H + 10 M + 2 F = $47. Also, it is given that 5 H + 9 M + F =$ 39 . 50. Then subtracting the following equations 6 H +10 M +2 F = $47 . 00 5 H +9 M + F = $39 . 50 yields H + M + F = $7 . 50. Multiplying the equation by 2 yields 2 H + 2 M + 2 F =$ 15 .