2023 AMC 10A Problems/Problem 8

Barb the baker has developed a new temperature scale for her bakery called the Breadus scale, which is a linear function of the Fahrenheit scale. Bread rises at 110 degrees Fahrenheit, which is 0 degrees on the Breadus scale. Bread is baked at 350 degrees Fahrenheit, which is 100 degrees on the Breadus scale. Bread is done when its internal temperature is 200 degrees Fahrenheit. What is this in degrees on the Breadus scale?

$\textbf{(A) }33\qquad\textbf{(B) }34.5\qquad\textbf{(C) }36\qquad\textbf{(D) }37.5\qquad\textbf{(E) }39$

Solution 1

To solve this question, you can use y = mx + b where the x is the Fahrenheit and the y is the Breadus. We have (110,0) and (350,100). We want to find (200,y). The slope for these two points is 5/12; y = 5x/12 + b. Solving for b using (110, 0), 550/12 = -b. We get b = -275/6. Plugging in (200, y), 1000/12-550/12=y. Simplifying, 450/12 = 37.5. $\boxed{(D)}$

~walmartbrian

Solution 2

Let $^\circ B$ denote degrees Breadus. We notice that $200^\circ F$ is $90^\circ F$ degrees to $0^\circ B$ , and $150^\circ F$ to $100^\circ B$ . This ratio is $90:150=3:5$ ; therefore, $200^\circ F$ will be $\dfrac3{3+5}=\dfrac38$ of the way from $0$ to $100$ , which is $\boxed{\text{(D) }37.5.}$

~Technodoggo

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2023 AMC 10A Problems/Problem 8

Solution 1

Solution 2