Difference between revisions of "1988 AJHSME Problems/Problem 18"
5849206328x (talk | contribs) (New page: ==Problem== The average weight of <math>6</math> boys is <math>150</math> pounds and the average weight of <math>4</math> girls is <math>120</math> pounds. The average weight of the <mat...) |
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==Problem== | ==Problem== | ||
| − | The average weight of <math>6</math> boys is <math>150</math> pounds and the average weight of <math>4</math> girls is <math>120</math> pounds. The average weight of the <math>10</math> children is | + | The [[average]] weight of <math>6</math> boys is <math>150</math> pounds and the average weight of <math>4</math> girls is <math>120</math> pounds. The average weight of the <math>10</math> children is |
<math>\text{(A)}\ 135\text{ pounds} \qquad \text{(B)}\ 137\text{ pounds} \qquad \text{(C)}\ 138\text{ pounds} \qquad \text{(D)}\ 140\text{ pounds} \qquad \text{(E)}\ 141\text{ pounds}</math> | <math>\text{(A)}\ 135\text{ pounds} \qquad \text{(B)}\ 137\text{ pounds} \qquad \text{(C)}\ 138\text{ pounds} \qquad \text{(D)}\ 140\text{ pounds} \qquad \text{(E)}\ 141\text{ pounds}</math> | ||
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\end{align*}</cmath> | \end{align*}</cmath> | ||
| − | We want the average of the <math>10</math> children, which is <cmath>\frac{S_B+S_G}{10}</cmath> From the first two equations, we can determine that <math>S_B=900</math> and <math>S_G=480</math>, so <math>S_B+S_G=1380</math>. Therefore, the average we desire is <cmath>\frac{1380}{10}=138 \rightarrow \boxed{\text{C}}</cmath> | + | We want the average of the <math>10</math> children, which is <cmath>\frac{S_B+S_G}{10}</cmath> From the first two [[equation|equations]], we can determine that <math>S_B=900</math> and <math>S_G=480</math>, so <math>S_B+S_G=1380</math>. Therefore, the average we desire is <cmath>\frac{1380}{10}=138 \rightarrow \boxed{\text{C}}</cmath> |
==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1988|num-b=17|num-a=19}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:56, 4 July 2013
Problem
The average weight of 
boys is 
pounds and the average weight of 
girls is 
pounds. The average weight of the 
children is
Solution
Let the boys have total weight 
and let the girls have total weight 
. We are given
We want the average of the children, which is ![\[\frac{S_B+S_G}{10}\]](http://latex.artofproblemsolving.com/d/c/e/dce7b314a87a068fb2b26143a04d72b68ad411c3.png)
From the first two equations, we can determine that 
and 
, so 
. Therefore, the average we desire is ![\[\frac{1380}{10}=138 \rightarrow \boxed{\text{C}}\]](http://latex.artofproblemsolving.com/7/0/a/70abfaa0ab3c280f9a027604833a3d5501e8f2e7.png)
See Also
| 1988 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 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. 
