The user-friendly version of this content is available here.
The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.
This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
At old MacDougall's farm there are only 20 horses and 24 cows left. They are being given 100 bushels of feed each day. MacDougall believes that "the animals are the business;" therefore, he has decided to increase the amount of feed given to the horses by 25% and the amount of feed given to the cows by 33.3% (repeating decimal). As a result of the increase, he now dispenses 124 bushels of feed a day. How many bushels of feed was each cow receiving before the increase?
Denote the number of bushels a horse was receiving before the increase with x and the number of bushels received by a cow with y. The situation before the increase is described algebraically as follows:
The situation after the increase is:
After simplification, the system of 2 equations with 2 unknowns (x and y) becomes:
We multiply the first equation by 6 and the second equation by 5 in order to get equal coefficients for x:
We subtract the first equation from the second one to eliminate the unknown x:
Finally, we get:
Before the increase, a cow was receiving 1.25 bushels of feed per day.