Difference between revisions of "1987 AJHSME Problems/Problem 16"
5849206328x (talk | contribs) (New page: ==Problem== Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting average was <math>40\% </math>. In he...) |
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==Problem== | ==Problem== | ||
| − | Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball | + | Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball season, so her seasonal shooting [[average]] was <math>40\% </math>. In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>. How many of these <math>10</math> shots did she make? |
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | ||
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==Solution== | ==Solution== | ||
| − | After the fourth game, she took <math>40</math> shots, <math>50\% </math> of which she made, so she made <math>40\times .5=20</math> shots. Twelve of them were made in the first three | + | After the fourth game, she took <math>40</math> shots, <math>50\% </math> of which she made, so she made <math>40\times .5=20</math> shots. Twelve of them were made in the first three games, so in the last game she made <math>20-12=8</math> shots. |
<math>\boxed{\text{E}}</math> | <math>\boxed{\text{E}}</math> | ||
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==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1987|num-b=15|num-a=17}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 21:04, 9 June 2024
Problem
Joyce made 
of her first 
shots in the first three games of this basketball season, so her seasonal shooting average was 
. In her next game, she took 
shots and raised her seasonal shooting average to 
. How many of these shots did she make?
Solution
After the fourth game, she took 
shots, of which she made, so she made 
shots. Twelve of them were made in the first three games, so in the last game she made 
shots.
See Also
| 1987 AJHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
