Difference between revisions of "1995 AHSME Problems/Problem 4"
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==Solution 2== | ==Solution 2== | ||
− | + | Alternately, picking an arbitrary value for <math>Q</math> of <math>100</math>, we find that <math>M = 30\% \cdot 100 = 0.30 \cdot 100 = 30</math>. | |
We find that <math>Q = 20\% \cdot P</math>, meaning <math>100 = 0.2\cdot P</math>, giving <math>P = \frac{100}{0.2} = \frac{1000}{2} = 500</math>. | We find that <math>Q = 20\% \cdot P</math>, meaning <math>100 = 0.2\cdot P</math>, giving <math>P = \frac{100}{0.2} = \frac{1000}{2} = 500</math>. |
Revision as of 21:09, 16 February 2018
Contents
[hide]Problem
If is of , is of , and is of , then
Solution 1
We are given: , , . We want M in terms of N, so we substitute N into everything:
Solution 2
Alternately, picking an arbitrary value for of , we find that .
We find that , meaning , giving .
Finally, since is of , we have .
Thus, and , so their ratio
This method does not prove that the answer must be constant, but it proves that if the answer is a constant, it must be .
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.