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Difference between revisions of "2019 AMC 12A Problems/Problem 2"

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==Solution 3 (Like Solution 1)==
 
==Solution 3 (Like Solution 1)==
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<math>a = 1.5b</math>. Multiply by 2 to obtain <math>2a = 3b</math>. Since <math>2 = 200\%</math>, the answer is <math>\boxed{200\% \implies D}</math>
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<math>a = 1.5b</math>. Multiply by 2 to obtain <math>2a = 3b</math>. Since <math>2 = 200\%</math>, the answer is <math>\boxed{\textbf{(D) }200\%}</math>.
  
 
-DBlack2021
 
-DBlack2021
 +
 +
==Solution 4 (Like Solution 2)==
 +
WLOG, let <math>b=2</math>. Then, we have <math>a=3</math> and <math>3b=6</math>.  Thus, <math>\frac{3b}{a}=\frac{6}{3}=2</math> so <math>3b</math> is <math>200\%</math> of <math>a</math> so the answer is <math>\boxed{\textbf{(D) }200\%}</math>.
  
 
==See Also==
 
==See Also==

Revision as of 22:37, 14 February 2019

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 $\boxed{D}.$

-21jzhang

Solution 3 (Like Solution 1)

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

-DBlack2021

Solution 4 (Like Solution 2)

WLOG, let $b=2$. Then, we have $a=3$ and $3b=6$. Thus, $\frac{3b}{a}=\frac{6}{3}=2$ so $3b$ is $200\%$ of $a$ so the answer is $\boxed{\textbf{(D) }200\%}$.

See Also

2019 AMC 12A (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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All AMC 12 Problems and Solutions

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