2019 AMC 12A Problems/Problem 2

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 $b=\frac{a}{1.5}$. We multiply by $3$ to get a $3b$ term, yielding $3b=2a$, and $2a$ is $\boxed{\textbf{(D) }200\%}$ of $a$.

Solution 2

Without loss of generality, let $b=100$. Then, we have $a=150$ and $3b=300$. Thus, $\frac{3b}{a}=\frac{300}{150}=2$, so $3b$ is $200\%$ of $a$. Hence the answer is $\boxed{\textbf{(D) }200\%}$.

Solution 3 (similar to Solution 1)

As before, $a = 1.5b$. Multiply by 2 to obtain $2a = 3b$. Since $2 = 200\%$, the answer is $\boxed{\textbf{(D) }200\%}$.

Solution 4 (similar to Solution 2)

Without loss of generality, let $b=2$. Then, we have $a=3$ and $3b=6$. This gives $\frac{3b}{a}=\frac{6}{3}=2$, so $3b$ is $200\%$ of $a$, so the answer is $\boxed{\textbf{(D) }200\%}$.

See Also

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

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