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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:

equation

The situation after the increase is:

equation

which becomes:

equation

After simplification, the system of 2 equations with 2 unknowns (x and y) becomes:

equation
equation

We multiply the first equation by 6 and the second equation by 5 in order to get equal coefficients for x:

equation
equation

We subtract the first equation from the second one to eliminate the unknown x:

equation

Finally, we get:

equation

Before the increase, a cow was receiving 1.25 bushels of feed per day.