HMMT 十一月 2014 · 冲刺赛 · 第 3 题

HMMT November 2014 — Guts Round — Problem 3

[ 5 ] Victoria wants to order at least 550 donuts from Dunkin’ Donuts for the HMMT 2014 November contest. However, donuts only come in multiples of twelve. Assuming every twelve donuts cost $7 . 49, what is the minimum amount Victoria needs to pay, in dollars? (Because HMMT is affiliated with MIT, the purchase is tax exempt. Moreover, because of the size of the order, there is no delivery fee.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT NOVEMBER 2014, 15 NOVEMBER 2014 — GUTS ROUND Organization Team Team ID#

解析

[ 5 ] Victoria wants to order at least 550 donuts from Dunkin’ Donuts for the HMMT 2014 November contest. However, donuts only come in multiples of twelve. Assuming every twelve donuts cost $7 . 49, what is the minimum amount Victoria needs to pay, in dollars? (Because HMMT is affiliated with MIT, the purchase is tax exempt. Moreover, because of the size of the order, there is no delivery fee.) Answer: 344.54 The smallest multiple of 12 larger than 550 is 552 = 12 · 46. So the answer is 46 · $7 . 49. To make the multiplication easier, we can write this as 46 · ($ 7 . 5 − $0 . 01) =$ 345 − $0 . 46 = $344 . 54. Note: this is the actual cost of donuts at the 2014 HMMT November contest.