2020 AMC 10A Problems/Problem 1

Problem

What value of $x$ satisfies \[x- \frac{3}{4} = \frac{5}{12} - \frac{1}{3}?\]

$\textbf{(A)}\ -\frac{2}{3}\qquad\textbf{(B)}\ \frac{7}{36}\qquad\textbf{(C)}\ \frac{7}{12}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{5}{6}$

Solution

Adding $\frac{3}{4}$ to both sides, $x= \frac{5}{12} - \frac{1}{3} + \frac{3}{4} = \frac{5}{12} - \frac{4}{12} + \frac{9}{12}=\boxed{\textbf{(E) }\frac{5}{6}}$.

Solution 2

Multiplying $12$ on both sides gets us $12x-9=1$, therefore $\boxed{x=\textbf{(E)}~\frac{5}{6}}$. ~CoolJupiter

Video Solution

Education, The Study of Everything

https://youtu.be/4lsmGWDYusk

~IceMatrix https://youtu.be/WUcbVNy2uv0


https://www.youtube.com/watch?v=7-3sl1pSojc

~bobthefam


https://youtu.be/OKoBg15l8ro

~savannahsolver

See Also

2020 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All AMC 10 Problems and Solutions

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