Difference between revisions of "1985 AJHSME Problems/Problem 16"

(New page: ==Problem== The ratio of boys to girls in Mr. Brown's math class is <math>2:3</math>. If there are <math>30</math> students in the class, how many more girls than boys are in the class? ...)
 
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==Problem==
 
==Problem==
  
The ratio of boys to girls in Mr. Brown's math class is <math>2:3</math>.  If there are <math>30</math> students in the class, how many more girls than boys are in the class?
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The [[ratio]] of boys to girls in Mr. Brown's math class is <math>2:3</math>.  If there are <math>30</math> students in the class, how many more girls than boys are in the class?
  
 
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 10</math>
 
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 10</math>
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Let the number of boys be <math>2x</math>, it follows that the number of girls is <math>3x</math>. These two values add up to <math>30</math> students, so <cmath>2x+3x=5x=30\Rightarrow x=6</cmath>
 
Let the number of boys be <math>2x</math>, it follows that the number of girls is <math>3x</math>. These two values add up to <math>30</math> students, so <cmath>2x+3x=5x=30\Rightarrow x=6</cmath>
  
The difference between the number of girls and the number of boys is <math>3x-2x=x</math>, which is <math>6</math>, so <math>\boxed{\text{D}}</math>
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The [[subtraction|difference]] between the number of girls and the number of boys is <math>3x-2x=x</math>, which is <math>6</math>, so <math>\boxed{\text{D}}</math>
  
 
==See Also==
 
==See Also==
  
[[1985 AJHSME Problems]]
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{{AJHSME box|year=1985|num-b=15|num-a=17}}
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[[Category:Introductory Algebra Problems]]

Revision as of 10:25, 16 May 2009

Problem

The ratio of boys to girls in Mr. Brown's math class is $2:3$. If there are $30$ students in the class, how many more girls than boys are in the class?

$\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 10$

Solution

Let the number of boys be $2x$, it follows that the number of girls is $3x$. These two values add up to $30$ students, so \[2x+3x=5x=30\Rightarrow x=6\]

The difference between the number of girls and the number of boys is $3x-2x=x$, which is $6$, so $\boxed{\text{D}}$

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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