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A farmer bought a number of pigs for $203. However, 6 of them died before he could sell the rest at a profit of 4 per pig.
His total profit was $50. How many pigs did he originally buy?
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Let "x" be the unknown number of pigs he originally bought, and
let "p" be the original price for each individual pig.
Then you have these two equations
xp = 203 (1)
(x-6)*(p+4) = 203+50 (2)
Simplify (2):
xp - 6p + 4x - 24 = 203 + 50
203 -6p + 4x - 24 = 203 + 50
-6p + 4x - 24 = 50
-6p + 4x = 50 + 24 = 74
-3p + 2x = 37.
Finally, you have these two equations
xp = 203
-3p + 2x = 37.
Express p from the second equation p = and substitute it into he first.
You will get a quadratic equation for the single unknown "x".
x*(2x-37) = 203*3 = 609.
Solve it and get the answer x= 29.
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Notice. Other setup/setups are possible, too. For example, this one:
- = 4.