2023 AMC 10A Problem 8

Problem 8 of 25EasierAlgebra

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?

Show solution

Solution

The Breadus reading is linear in Fahrenheit through

(110, 0)

and

(350, 100),

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.

Tagged: linear equation · slope