Difference between revisions of "1994 AJHSME Problems/Problem 11"
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<math>\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52</math> | <math>\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52</math> | ||
| + | |||
| + | ==Solution== | ||
| + | Make a table with the information given. | ||
| + | |||
| + | <cmath>\begin{tabular}{c|ccc} | ||
| + | & \text{Jonas} & \text{Clay} & \text{total} \\ \hline | ||
| + | \text{boys} & & & 52 \\ | ||
| + | \text{girls} & 20 & & 48 \\ | ||
| + | \text{total} & 40 & 60 & 100 | ||
| + | \end{tabular}</cmath> | ||
| + | |||
| + | Because the first two columns must add up to the third column, and the same with the rows, the rest of the empty boxes can be filled in. | ||
| + | |||
| + | <cmath>\begin{tabular}{c|ccc} | ||
| + | & \text{Jonas} & \text{Clay} & \text{total} \\ \hline | ||
| + | \text{boys} & 20 & 32 & 52 \\ | ||
| + | \text{girls} & 20 & 28 & 48 \\ | ||
| + | \text{total} & 40 & 60 & 100 | ||
| + | \end{tabular}</cmath> | ||
| + | |||
| + | The number of boys from Clay is <math>\boxed{\text{(B)}\ 32}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1994|num-b=10|num-a=12}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:13, 4 July 2013
Problem
Last summer 
students attended basketball camp. Of those attending, 
were boys and 
were girls. Also, 
students were from Jonas Middle School and 
were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?
Solution
Make a table with the information given.
![\[\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & & & 52 \\ \text{girls} & 20 & & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}\]](http://latex.artofproblemsolving.com/4/e/a/4eac8423a86a41425df1c3d6f3d1b8dc5dcfc034.png)
Because the first two columns must add up to the third column, and the same with the rows, the rest of the empty boxes can be filled in.
![\[\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & 20 & 32 & 52 \\ \text{girls} & 20 & 28 & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}\]](http://latex.artofproblemsolving.com/d/f/0/df0fe33721b6b6ffaedcdb960dcd634a5c3100a1.png)
The number of boys from Clay is 
.
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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. 
