Question 1165699: A farmer buys 100 animals for $100 total. The animals include at least 1 cow, 1 pig and 1 chicken. A cow costs $10, a pig costs $3 and a chicken costs $0.50. If the farmer buys 5 times as many cows as pigs, how many of each animal does he buy?
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
A farmer buys 100 animals for $100 total. The animals include at least 1 cow, 1 pig and 1 chicken.
A cow costs $10, a pig costs $3 and a chicken costs $0.50. If the farmer buys 5 times as many cows as pigs, how many of each animal does he buy?
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Let x be the number of pigs.
Then the number of cows is 5x and the number of chicken is 100-x-5x = 100-6x.
Then the total money equation is
10*(5x) + 3*x + 0.50*(100-6x) = 100 dollars.
Simplify and solve
50x + 3x + 50 - 3x = 100
50x = 50
x = 50/50 = 1 is the number of pigs.
ANSWER. 1 pig, 5 cows and 100-1-5 = 94 chicken.
Solved.
A miracle is that this problem can be solved using one single equation in one single unknown.
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