Math Word Problem

Question

An investor invested a total of $2,700 in two mutual funds. One fund earned a 8% profit while the other earned a 6% profit. If the investor's total profit was $188, how much was invested in each mutual fund?

Answer 1

Hi Ashley.

 

This problem deals with two different mutual funds which collect interest at 2 different rates. We're going to set up a system of equations to determine these.

 

The first step in setting up system of equations problems is calling very specific and well-defined variables.

 

I'm going to call variables E and S.

 

E = amount of money in the eight percent account

S = amount of money in the six percent account

 

There's a total of $2,700 invested between the two accounts. That means that the amount of money in the eight percent account plus the amount of money in the six percent account equals $2,700.

 

E + S = 2700

 

It also says the total profit was $188. We know that E collects interest at 8% and S collects interest at 6%. So, the amount of money in E times its interest rate plus the amount of money in S times its interest will equal a grand total of $188.

 

0.08*E + 0.06*S = 188

 

Now you have two equations, two unknowns.

 

E + S = 2700

0.08E + 0.06S = 188

 

Multiply the bottom equation by 100 to clear the decimals.

 

E + S = 2700

8E + 6S = 18800

 

Multiply the top equation by -6 then add the two equations together to eliminate S.

 

-6E - 6S = -16200

8E + 6S = 18800

 

2E = 2600

 

E = 1300

 

If E = 1300, and E + S = 2700, then S = 1400.

 

Always good to double check your results:

 

1300 + 1400 = 2700. Check.

 

1300(0.08) + 1400(0.06)

 

= 104 + 84 = 188. Check.

 

Hope this helps.