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

(Created page with "Suppose that <math>a * b</math> means <math>3a-b.</math> What is the value of <math>x</math> if <cmath>2 * (5 * x)=1</cmath> <math>\textbf{(A) }\frac{1}{10} \qquad\textbf{(B)...")
 
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==Solution==
 
==Solution==
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Let us plug in <math>(5 * x)=1</math> into <math>3a-b</math>. Thus it would be <math>3(5)-x</math>. Now we have <math>2*(15-x)=1</math>. Plugging <cmath>2*(15-x)</cmath>into <math>3a-b</math>. We have <math>6-15+x=1</math>. Solving for <math>x</math> we have <cmath>-9+x=1</cmath><cmath>x=\boxed{\textbf{(D)} 10}</cmath>

Revision as of 09:42, 23 November 2016

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

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 \[-9+x=1\]\[x=\boxed{\textbf{(D)} 10}\]

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