2016 AMC 8 Problem 10 — Solution & Video | LIVE by Po-Shen Loh

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2016 AMC 8 Problem 10

Attempt Problem 10 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

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

$\dfrac{1}{10}$

$2$

$\dfrac{10}{3}$

$10$

$14$

Answer: D

Concepts:custom operation linear equation

Difficulty rating: 1030

Video solution:

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Written solution:

First, $5\ast x=15-x$ . Applying the operation again gives $\begin{aligned} 2\ast(15-x)&=6-(15-x)\\ &=x-9. \end{aligned}$ Thus $x-9=1$ , so $x=10$ .

Thus, D is the correct answer.

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