Question

面包师 Barb 为她的面包店设计了一种新的温度刻度，叫作 Breadus 刻度，它是华氏温度的线性函数。面包在华氏 $110\text{ F}^{\circ}$ 度时发酵，这对应 Breadus 刻度的 $0$ 度。面包在华氏 $350\text{ F}^{\circ}$ 度时烘烤，这对应 Breadus 刻度的 $100$ 度。面包完成时内部温度为华氏 $200\text{ F}^{\circ}$ 度。这在 Breadus 刻度中是多少度？

Barb the baker creates a new temperature system for baking bread, Breadus, which is linearly based on Fahrenheit. Bread rises at $110\text{ F}^{\circ},$ which is $0$ on the Breadus scale. Bread bakes at $350\text{ F}^{\circ},$ which is $100$ on the Breadus scale. Bread is done when its internal temperature is $200\text{ F}^{\circ}.$ What is this temperature on the Breadus scale?

$33$

$34.5$

$36$

$37.5$

$39$

答案：D

知识点：一次方程斜率

难度评级：1130

解答：

Breadus 读数是经过 $(110, 0)$ 和 $(350, 100)$ 的华氏温度线性函数，所以 $B = \frac{100}{350 - 110}(F - 110)$ $= \frac{5}{12}(F - 110)$ 。代入 $F = 200$ ： $B = \frac{5}{12} \cdot 90 = 37.5$ 。因此，答案是 D。

The Breadus reading is linear in Fahrenheit through $(110, 0)$ and $(350, 100),$ so $B = \frac{100}{350 - 110}(F - 110)$ $= \frac{5}{12}(F - 110).$ Plug in $F = 200:$ $B = \frac{5}{12} \cdot 90 = 37.5.$ Therefore, the answer is D.

2023 AMC 10A 第 8 题

答案：D

难度评级：1130

解答：

其他年份的第 8 题