Difference between revisions of "1964 AHSME Problems/Problem 14"
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Let us say each sheep cost <math>x</math> dollars. The farmer paid <math>749x</math> for the sheep. He sold <math>700</math> of them for <math>749x</math>, so each sheep sold for <math>\frac{749}{700} = 1.07x</math>. | Let us say each sheep cost <math>x</math> dollars. The farmer paid <math>749x</math> for the sheep. He sold <math>700</math> of them for <math>749x</math>, so each sheep sold for <math>\frac{749}{700} = 1.07x</math>. | ||
| − | Since every sheep sold for the same price per head, and since every sheep cost <math>x</math> and sold for <math>1.07x</math>, there is an increase of <math>\frac{1.07x - 1x}{1x} = 0.07</math>, or <math>7\%</math>, which is option <math>\ | + | Since every sheep sold for the same price per head, and since every sheep cost <math>x</math> and sold for <math>1.07x</math>, there is an increase of <math>\frac{1.07x - 1x}{1x} = 0.07</math>, or <math>7\%</math>, which is option <math>\boxed{\textbf{(C)}}</math> |
==See Also== | ==See Also== | ||
Latest revision as of 17:33, 23 July 2019
Problem
A farmer bought 
sheep. He sold 
of them for the price paid for the sheep.
The remaining 
sheep were sold at the same price per head as the other .
Based on the cost, the percent gain on the entire transaction is:
Solution
Let us say each sheep cost 
dollars. The farmer paid 
for the sheep. He sold of them for , so each sheep sold for 
.
Since every sheep sold for the same price per head, and since every sheep cost and sold for 
, there is an increase of 
, or 
, which is option 
See Also
| 1964 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
