Difference between revisions of "1998 AJHSME Problems/Problem 14"
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| − | ==Problem | + | ==Problem== |
An Annville Junior High School, <math>30\%</math> of the students in the Math Club are in the Science Club, and <math>80\%</math> 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? | An Annville Junior High School, <math>30\%</math> of the students in the Math Club are in the Science Club, and <math>80\%</math> 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? | ||
| Line 5: | Line 5: | ||
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 40</math> | <math>\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 40</math> | ||
| + | ==Solution== | ||
| − | = | + | 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. |
| − | + | These <math>12</math> people are also <math>30\%</math> of the Math Club. | |
| − | + | Setting up a proportion: | |
| − | <math>12= | + | <math>\frac{12}{30\%} = \frac{x}{100\%}</math> |
| − | <math> | + | <math>12\cdot 1.00 =0.30\cdot x</math> |
| − | <math>40= | + | <math>\frac{12}{0.3} = 40=x </math> |
There are <math>40=\boxed{E}</math> people in the Math Club. | There are <math>40=\boxed{E}</math> people in the Math Club. | ||
| − | |||
== See also == | == See also == | ||
| − | {{AJHSME box|year=1998| | + | {{AJHSME box|year=1998|num-b=13|num-a=15}} |
* [[AJHSME]] | * [[AJHSME]] | ||
* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Revision as of 00:32, 5 July 2013
Problem
An Annville Junior High School, 
of the students in the Math Club are in the Science Club, and 
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?
Solution
If of the people in the science club of 
people are in the Math Club, 
people are in the both the Math Club and the Science Club.
These 
people are also of the Math Club.
Setting up a proportion:
There are 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
