Algebra 1 Word Problem

Question

An investor invested a total of $1,800 in two mutual funds. One fund earned a 55 % profit while the other earned a 22 % profit. If the investor's total profit was $72, how much was invested in each mutual fund?'

 

The amount invested in the mutual fund that earned 55 % was what?

Answer 1

First, note that a 22% profit on $1800 is $396, while a 55% profit on $1800 would be $990.  So, $396 and $990 represent the extreme ends of the range of what he could've earned by splitting his money between the two funds.  Therefore, we expect that we'd have to have unrealistic input in order to end up with $72 profit.  I assume there's a typo somewhere in the problem, but I'll solve it anyway to show you how the equations are set up.

 

Let the amount in the first be A and the amount in the second be B.  Then we have:

 

A+B = 1800

.55*A + .22*B = 72

 

If we solve the first equation for A, we get:

 

A = 1800 - B

 

Substituting this into the second equation, we get:

 

.55(1800 - B) + .22*B = 72

990 - .55B + .22B = 72

990 - 72 = .33B

B = 2781

A = 1800 - 2781 = -981

 

Therefore, he would have needed to invest negative $981 in the first fund and positive $2781 in the second fund.  This isn't allowed under normal rules, but then again, we did anticipate an unrealistic answer.

 

If you have additional questions on word problems or systems of equations, feel free to let me know.