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Difference between revisions of "1994 AJHSME Problems/Problem 11"

(Created page with "==Problem== Last summer <math>100</math> students attended basketball camp. Of those attending, <math>52</math> were boys and <math>48</math> were girls. Also, <math>40</math>...")
 
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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
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\text{boys} & & & 52 \\
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\text{girls} & 20 & & 48 \\
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\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 \\
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\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}}

Revision as of 23:36, 22 December 2012

Problem

Last summer $100$ students attended basketball camp. Of those attending, $52$ were boys and $48$ were girls. Also, $40$ students were from Jonas Middle School and $60$ were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?

$\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52$

Solution

Make a table with the information given.

\[\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & & & 52 \\ \text{girls} & 20 & & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}\]

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.

\[\begin{tabular}{c|ccc} & \text{Jonas} & \text{Clay} & \text{total} \\ \hline \text{boys} & 20 & 32 & 52 \\ \text{girls} & 20 & 28 & 48 \\ \text{total} & 40 & 60 & 100 \end{tabular}\]

The number of boys from Clay is $\boxed{\text{(B)}\ 32}$.

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
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