2019 AMC 12A Problems/Problem 2

Revision as of 09:09, 10 February 2019 by Jzhang21 (talk | contribs) (Solution)

Problem

Suppose $a$ is $150\%$ of $b$. What percent of $a$ is $3b$?

$\textbf{(A) } 50 \qquad \textbf{(B) } 66\frac{2}{3} \qquad \textbf{(C) } 150 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 450$

Solution 1

Since $a=1.5b$, that means $b=a/1.5$. We multiply by 3 to get a $3b$ term, to yield $3b=2a$.

$2a$ is $\boxed{200\%}$ of $a$.

-- eric2020

Solution 2

WLOG, let $b=100$. Then, we have $a=150$ and $3b=300$. Thus, $\frac{3b}{a}=\frac{300}{150}=2$ so $3b$ is $200\%$ or $a$ so the answer is $\boxed{D}.$

See Also

2019 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AMC 12 Problems and Solutions

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