2016 CEMC Gauss (Grade 8) Problems/Problem 9

Problem

$10\%$ of $200$ is equal to $20\%$ of

$\textbf{(A)}\ 40 \qquad\textbf{(B)}\ 50 \qquad\textbf{(C)}\ 100 \qquad\textbf{(D)}\ 400 \qquad\textbf{(E)}\ 800$

Solution 1

First, we can figure out what $10\%$ of $200$ is. This would be $10\% \times 200 = \frac{1}{10} \times 200 = 20$

Next, we can let $x$ be the missing number. Setting up an equation, we have:

$20\% \times x = 20$

$\frac{1}{5} \times x = 20$

$x = 20 \times 5 = \boxed {\textbf {(C) } 100}$

~anabel.disher

Solution 2

For the values to be equal, the missing number must be half of $200$ for the values to be equal because $10\% \times 2 = 20\%$ , so halving $200$ would cancel out the $\times 2$ .

This shows that the missing number is $\frac{200}{2} = \boxed {\textbf {(C) } 100}$

~anabel.disher

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2016 CEMC Gauss (Grade 8) Problems/Problem 9

Problem

Solution 1

Solution 2