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2016 AMC 8 Problems/Problem 10: Difference between revisions

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==Solution 2==
==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>
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/cR1GDMq1Cv4?si=KktuZcPdJxqC83rg
A solution so simple that a 12-year-old made it!
~Elijahman~


==Video Solution (CREATIVE THINKING!!!)==
==Video Solution (CREATIVE THINKING!!!)==
Line 16: Line 24:


~Education, the Study of Everything
~Education, the Study of Everything


==Video Solution==
==Video Solution==
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{{AMC8 box|year=2016|num-b=9|num-a=11}}
{{AMC8 box|year=2016|num-b=9|num-a=11}}
{{MAA Notice}}
{{MAA Notice}}
[[Category:Introductory Algebra Problems]]

Latest revision as of 17:04, 25 June 2025

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/cR1GDMq1Cv4?si=KktuZcPdJxqC83rg

A solution so simple that a 12-year-old made it!

~Elijahman~

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/0FhGMy0mCVU

~Education, the Study of Everything

Video Solution

https://youtu.be/ysYNhG_uG-I

~savannahsolver

Video Solution by OmegaLearn

https://youtu.be/TkZvMa30Juo?t=638

~pi_is_3.14

See Also

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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