Search 75,802 tutors
FIND TUTORS
Ask a question
0 0

invester invests 2,200 in 2 mutual funds 1 earns 4% other2% profit was $76 how much was invested in each fund?

Tutors, please sign in to answer this question.

2 Answers

We can set up two equations to solve for our two unknowns.
One equation based on the amounts invested (x + y = 2200).
The other equation based on the interest yield for each investment (.04x + .02y = 76).
Now we can substitute an expression for one variable in terms of the other variable from the first equation and plug that expression into the second equation like this:  .04x + .02(2200 - x) = 76.
Now we can solve for x (our 1st variable) as follows:
    1.  4x + 2(2200 - x) = 7600 (multiplied each term on both sides by 100 to get rid of the decimals).
    2.  4x + 4400 - 2x = 7600 (did the multiplication on the left side).
    3.  2x + 4400 = 7600 (combined our x terms on the left side).
    4.  2x = 7600 - 4400 (subtracted 4400 from both sides to isolate the variable on the left side).
    5.  2x = 3200 (did the subtraction on the left side).
    6.  x = 1600 (divided both sides by 2 to get our value for x - amount invested at 4 percent).
Now we can subtract our value for x from the total investment of 2200 dollars to get our value for y (amount invested at 2 percent), which gives 600 (2200 - 1600).     

You can set your problem up like this:

We'll say A is the money invested in the 4% fund and B is the money invested into the 2% fund. They have to total $2200 so the equation would be
A + B = $2200 which can also be written A = 2200 - B or B = 2200 - A when solving for one fund.

The rest of the equation can be written this way:
Profit = 4% of A + 2% of B

or mathmatically:
76 = .04A + .02(2200-A)
76 = .04(2200-B) + .02B

After you get A or B, you should be able to get the other variable by plugging it into the top equation, and then multiply by the percent!