Difference between revisions of "2016 AMC 8 Problems/Problem 10"

Revision as of 09:28, 21 March 2022

Problem

Suppose that $a * b$ means $3a-b.$ What is the value of $x$ if $2 * (5 * x)=1$ $\textbf{(A) }\frac{1}{10} \qquad\textbf{(B) }2\qquad\textbf{(C) }\frac{10}{3} \qquad\textbf{(D) }10\qquad \textbf{(E) }14$

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

Video Solution

https://youtu.be/ysYNhG_uG-I

~savannahsolver

2016 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 11: / Line 11: @@
 ==Solution 2==
 Let us set a variable <math>y</math> equal to <math>5 * x</math>. Solving for y in the equation <math>3(2)-y=1</math>, we see that y is equal to five. By substitution, we see that <math>5 * x</math> = 5. Solving for x in the equation <math>5(3)-x = 5</math> we get <cmath>x=\boxed{\textbf{(D)}   \,        10}</cmath>
+==Video Solution==
+https://youtu.be/ysYNhG_uG-I
+~savannahsolver
 ==See Also==
 {{AMC8 box|year=2016|num-b=9|num-a=11}}
 {{MAA Notice}}

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