Question 284842: Sam Mathius invested part of his $10,000 bonus in a fund that paid an 11% profit and invested the rest in stock that suffered a 4% loss. Find the amount of each investment if his overall net profit is $650.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x equals amount he invested in the fund that paid 11% profit.
y equals the amount he invested in the fund that suffered a 4% loss.
His overall net profit was $650.
You have 2 equations to work with.
They are:
x + y = 10,000.
.11x - .04y = 650
You need to solve these 2 equations to get your answer.
solve for y in the first equation to get:
y = 10,000 - x.
Substitute that value for y in the second equation to get:
.11x - .04*(10,000 - x) = 650
Simplify to get:
.11x - .04*10,000 + .04x = 650
Combine like terms and simplify further to get:
.15x - 400 = 650
Add 400 to both sides of this equation to get:
.15x = 650 + 400
Combine like terms to get:
.15x = 1050
Divide both sides of this equation by .15 to get:
x = 7,000
Since x + y = 10,000, this means that y = 3,000
Your original equation is:
.11x - .04y = 650
Substitute 7,000 for x and 3,000 for y to get:
.11*7,000 - .04*3,000 = 650
Simplify to get:
770 - 120 = 650 confirming that the values for x and y are good.
He gained $770 from the 7,000 investment and he lost $120 from the 3,000 investment for a net profit of $650.00
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