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Difference between revisions of "1998 AJHSME Problems/Problem 14"

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If <math>80\%</math> of the people in the science club of <math>15</math> people are in the Math Club, <math>\frac{4}{5}\times15=12</math> people are in the both the Math Club and the Science Club.
 
If <math>80\%</math> of the people in the science club of <math>15</math> people are in the Math Club, <math>\frac{4}{5}\times15=12</math> people are in the both the Math Club and the Science Club.
  
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These <math>12</math> people are also <math>30\%</math> of the Math Club.
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These <math>12</math> people make up <math>30\%</math> of the Math Club.
  
 
Setting up a proportion:
 
Setting up a proportion:
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<math>\frac{12}{30\%} = \frac{x}{100\%}</math>
 
  
 
<math>12\cdot 1.00 =0.30\cdot x</math>
 
<math>12\cdot 1.00 =0.30\cdot x</math>
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* [[AJHSME Problems and Solutions]]
 
* [[AJHSME Problems and Solutions]]
 
* [[Mathematics competition resources]]
 
* [[Mathematics competition resources]]
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{{MAA Notice}}

Latest revision as of 00:11, 28 May 2021

Problem

An Annville Junior High School, $30\%$ of the students in the Math Club are in the Science Club, and $80\%$ of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?

$\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 40$

Solution

If $80\%$ of the people in the science club of $15$ people are in the Math Club, $\frac{4}{5}\times15=12$ people are in the both the Math Club and the Science Club.

These $12$ people make up $30\%$ of the Math Club.

Setting up a proportion:

$12\cdot 1.00 =0.30\cdot x$

$\frac{12}{0.3} = 40=x$

There are $40=\boxed{E}$ people in the Math Club.

See also

1998 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
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 AJHSME/AMC 8 Problems and Solutions

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