SOLUTION: 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 o

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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