SOLUTION: A man made a profit of P 290 by selling 8 cows and 14 calves at a gain of 25% of what they cost him. Had he sold 14 cows and 8 calves instead at the same percentage of profit, he w

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Question 347475: A man made a profit of P 290 by selling 8 cows and 14 calves at a gain of 25% of what they cost him. Had he sold 14 cows and 8 calves instead at the same percentage of profit, he would have gained P400. Find the original cost of each cow and each calf?
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = Cost of Cows

Let Y= Cost of Claves


=> 1/4 ( 8X + 14Y ) = 290

=> 8X + 14Y = 1160 ---------- A


=> 1/4 ( 14X + 8Y ) = 400

=> 14X + 8Y = 1600 ----------- B


=> Now try to eliminate one of the unknow values by using common factors

=> Multiply A by 4

=> 4 (8X + 14Y = 4 (1160 )

=> 32X + 56Y = 4640 --------- C

=> Multiply B by 7

=> 7 (14X + 8Y) = 7 (1600)

=> 98X + 56Y = 11200 ------- D


=> D - C

=> ( 98X + 56Y ) - ( 32X + 56Y ) = 11200 - 4640

=> 66X = 6560

=> X = 99.393939......

=> X = 99.40


=> Sub. X = 99.40 into A or any equations from above

=> 8X + 14Y = 1160

=> 8 (99.40) + 14Y = 1160

=> 795.20 + 14Y = 1160

=> 14Y = 1160 - 795.20

=> 14Y = 364.80

=> Y = 364.8 / 14

=> Y = 26.05714...

=> Y = 26.06


Answer: Original Cost for Cows $99.40 each, $26.06 for Calves each.