SOLUTION: Sandra invested $8000 in two mutual funds. At the end of the year, the percent return on one fund (x) was 8% and the percent return on the other fund (y) was 3%. The combined retur

Question 841563: Sandra invested $8000 in two mutual funds. At the end of the year, the percent return on one fund (x) was 8% and the percent return on the other fund (y) was 3%. The combined return on both funds was $345. Which system of equations can be used to find how much Sandra invested in each fund?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 2 equations to work with.
x + y = 8000 is your first equation.
.08x + .03y = 345 is your second equation.

you solve these equations simultaneously for x and y to get your answer.
you can do it by substitution or elimination.

i'll do it by elimination.

start with:

x + y = 8000
.08x + .03y = 345

multiply both sides of the second equation by -12.5 to get:

x + y = 8000
-x - .375y = -4312.5

add the 2 equations together to get:

y - .375y = 8000 - 4312.5
simplify to get:
.625y = 3687.5
divide both sides of this equation by .625 to get:
y = 3687.5/.625 = 5900

since x + y = 8000, then x must be equal to 2100 because 5900 and 2100 = 8000.

so you now have:
x = 2100 and y = 5900.

take .08 * 2100 and add it to .03 * 5900 to get 345.

numbers check out and your solution is good.

you can also solve it by substitution.

start with:

x + y = 8000
.08x + .03y = 345

solve for x in the first equation to get:

x = 8000 - y

substitute for x in the second equation to get:

.08(8000 - y) + .03y = 345

simplify to get:

640 - .08y + .03y = 345

combine like terms to get:

640 - .05y = 345

subtract 345 from both sides of this equation and add .05y to both sides of this equation to get:

640 - 345 = .05y
simplify to get:
295 = .05y
divide both sides of this equation by .05 to get:
y = 5900

your answer will be the same as the one you got through elimination.

you can also solve by graphing although the solution you get using that method may not be as exact.

the graphical solution is shown below:

the intersection point is the solution.
it's not easy to see, but i did verify with an other graphing calculator that it is x = 2100 and y = 5900.

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