AMC8 2022

AMC8 2022 · Q6

AMC8 2022 · Q6. It mainly tests Linear equations, Rates (speed).

Three positive integers are equally spaced on a number line. The middle number is $15,$ and the largest number is $4$ times the smallest number. What is the smallest of these three numbers?

三个正整数在数轴上等距分布。中间的数是$15$，最大的数是最小的数的$4$倍。这三个数中最小的数是多少？

(A) 4 4

(B) 5 5

(D) 7 7

(E) 8 8

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let the smallest number be $x.$ It follows that the largest number is $4x.$ Since $x,15,$ and $4x$ are equally spaced on a number line, we have \begin{align*} 4x-15 &= 15-x \\ 5x &= 30 \\ x &= \boxed{\textbf{(C) } 6}. \end{align*}

设最小的数为$x$。则最大的数为$4x$。因为$x,15,$和$4x$在数轴上等距分布，所以 \begin{align*} 4x-15 &= 15-x \\ 5x &= 30 \\ x &= \boxed{\textbf{(C) } 6}. \end{align*}

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