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Question 446476: A farmer buys cattle and sheep for an amount of $53800. He buys 100 animals in total. The sheep were $250 each and the cattle were $730 each.How many sheep and how many cattle did he buy in total?
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! x = number of cattle the farmer buys
100 - x = number of sheep the farmer buys (because if he buys 100 animals in total, and x of them are cattle, the remainder--100 - x-- is the number of sheep he buys)
$250*(the number of sheep) + $730*(the number of cattle) = $53800
250(100 - x) + 730x = 53800
Distribute: 25000 - 250x + 730x = 53800
Combine like terms: 25000 + 480x = 53800
Subtract 25000 from both sides: 480x = 28800
Divide both sides by 480: x = 60
THEREFORE, THE FARMER BOUGHT 60 CATTLE.
To find the number of sheep, plug 60 in for the value of x in the expression for the number of sheep (100 - x)
100 - 60 = 40
THEREFORE, THE FARMER BOUGHT 40 SHEEP.
==> THE FARMER BOUGHT 40 SHEEP AND 60 CATTLE.
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