AMC10 2023 A

AMC10 2023 A · Q8

AMC10 2023 A · Q8. It mainly tests Functions basics, Graphs (coordinate plane).

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?

面包师Barb为她的面包店开发了一种新的温度标度，称为Breadus标度，它是华氏标度的线性函数。面包在$110$华氏度时发酵，这对应Breadus标度的$0$度。面包在$350$华氏度时烘烤，这对应Breadus标度的$100$度。面包内部温度达到$200$华氏度时完成烘烤。这在Breadus标度上是多少度？

(A) 33 33

(B) 34.5 34.5

(D) 37.5 37.5

(E) 39 39

Answer

Correct choice: (D)

正确答案：（D）

Solution

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

解此题可以使用$f(x) = mx + b$，其中$x$为华氏度，$y$为Breadus度。我们有点$(110,0)$和$(350,100)$。我们想找到点$(200,y)$上$y$的值，这条直线上。两点斜率为$\frac{5}{12}$；$y = \frac{5}{12}x + b$。使用$(110, 0)$解$b$，$\frac{550}{12} = -b$。我们得到$b = \frac{-275}{6}$。代入$(200, y)$，$\frac{1000}{12}-\frac{550}{12}=y$。简化，$\frac{450}{12} = \boxed{\textbf{(D) }37.5}$

Topics