2016 AMC 8

Complete problem set with solutions and individual problem pages

Problem 10 Easy

Suppose that a * b means 3a-b. What is the value of x if

2 * (5 * x)=1

  • A.

    \frac{1}{10}

  • B.

    2

  • C.

    \frac{10}{3}

  • D.

    10

  • E.

    14

Answer:D

Solution 1

Let us plug in (5 * x)=1 into 3a-b. Thus it would be 3(5)-x. Now we have 2*(15-x)=1. Plugging 2*(15-x) into 3a-b, we have 6-15+x=1. Solving for x we have

-9+x=1

x=\boxed{\textbf{(D)} \, 10}

 

Solution 2

Let us set a variable y equal to 5 * x. Solving for y in the equation 3(2)-y=1, we see that y is equal to five. By substitution, we see that 5 * x = 5. Solving for x in the equation 5(3)-x = 5 we get

x=\boxed{\textbf{(D)} \, 10}

Related Problems
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