AMC8 2016

AMC8 2016 · Q10

AMC8 2016 · Q10. It mainly tests Linear equations, Functions basics.

Suppose that $a * b$ means $3a - b$. What is the value of $x$ if $2*(5*x) = 1$?

假设$a * b$表示$3a - b$。若$2*(5*x) = 1$，则$x$的值是多少？

(A) $1/10$ $1/10$

(B) 2 2

(D) 10 10

(E) 14 14

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since $2 \ast (5 \ast x) = 1$, it follows that $6-(5 \ast x) = 1$, and so $5 \ast x = 5$. Applying the formula again, $15-x = 5$, and therefore $x = 10$.

由于 $2 \ast (5 \ast x) = 1$，于是 $6-(5 \ast x) = 1$，从而 $5 \ast x = 5$。再次应用该公式，$15-x = 5$，因此 $x = 10$。

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