SOLUTION: What is the solution for the following word problem? An investor invested a total of $2500 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. I

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Question 651623: What is the solution for the following word problem?
An investor invested a total of $2500 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor's total profit was $65, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 5% = ?
The amount invested in the mutual fund that earned 2% = ?
Work I have attempted on the problem:
$2500/5% = $125.00 profit
$2500/2% = $50.00 profit
Amount invested in each mutual fund is $65/2 = $32.50 profit
Am I on the right track?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = amount invested at 5%
let y = amount invested at 2%
you have 2 equations.
x + y = 2500
.05x + .02y = 65
the first equation states that the total money invested is 2500.
the second equation states that the total profit is equal to 65.
these are 2 equations that need to be solved simultaneously.
simples way to solve is by substitution.
solve for y in the first equation to get:
y = 2500 -x
substitute that value for y in the second equation to get:
.05x + .02(2500-x) = 65
what you have done is reduce the problem to 1 equation in 1 unknown that can be solved easily.
simplify that equation to get:
.05x + .02(2500) - .02x = 65
simplify to get:
.05x + 50 - .02x = 65
combine like terms to get:
.03x + 50 = 65
subtract 50 from both sides of the equation to get:
.03x = 15
divide both sides of the equation by .03 to get:
x = 15/.03 = 500
since x + y = 2500 and x = 500, the equation becomes:
500 + y = 2500
solve for y to get y = 2000
you solution is x = 500 and y = 2000
test the solution by substituting in the original equations.
x + y becomes 500 + 2000 becomes 2500 which is equal to the total money invested so that part is good.
.05x + .02y = 65 becomes .05(500) + .02(2000) which becomes 25 + 40 which becomes 65 which is equal to the total interest earned so that part is good.
x = 500 and y = 2000 is your solution.