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Question 6410: Could you please help me solve this problem. It got me so confused while trying it that I've been working on it for 2 weeks.
Anita invested a total of $5000 at the beginning of the year in two different funds. At the end of the year, her investment had grown to $5531. The money in the first fund earn 9%, while the money in the second fund earned 13.5%. How much of the $5000 was invested in each fund at the beginning of the year? Use a system of equations to solve this problem.
Answer by digitalbeachbum(7)   (Show Source):
You can put this solution on YOUR website! Hello,
The issue is setting the problem correctly. I tried it several times before I got it correct (with some help).
Step 1: Setup the problem
.135(x) + .09(5000-x) = 531
The way this is set up is to take the percentage, covert them to decimal, then multiple them by X. Except that one of the two must include 5000-x because that is the amount that was invested at the begining of the year subtracted from the orignal $5000. This equation is = to 531 because that is the profit received from the % of the two accounts. You don't use $5000 because that is the inital investment (this is where I messed up originally).
Step 2: Combine like terms
.135x + 450 - .090x = 531
Multiply .09 in to (5000-x) and then combine all values with X. You are left with what you see above.
Step 3: Solve for X
.045x = 81
Divide both sides by .045
x=81/.045 = $1800 at 13.5%
Since you set the problem up with 13.5% with X your solution ends up being X at 13.5%.
The remainder of the total amount is applied to (5000-x) at 9%
5000-x = $3200 at 9%
Hope this helps.
Thanks to R^2 for his assistance!
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