Expert: Abe Mantell - 1/10/2012

Question
I'm stumped on a word problem with elimination using multiplication. It's adding in percents and money and I'm not sure how to get the answer. The problem is:

Gunther invested $10,000 in 2 mutual funds. One of the funds rose 6% in one year and the other rose 9% in one year. If Gunther's investment rose to a total of $684 in one year how much did he invest in each mutual fund?

Thanks!

Answer
Hello Lexi,

This can be done with only one variable, but since you mentioned elmination,
I gather you need to use two variables, so...

Let x=$ that increased by 6% and y=$ that increased by 9%

Thus, we get the two equations:
1. x+y=10000
2. 0.06x+0.09y=684

Multiply equation (2) by 100 to get: 6x+9y=68400
and multiply equation (1) by -6 to get: -6x-6y=-60000
Now add the two, to get: 3y=8400, so y=2800...thus, x=7200

Therefore, $7200 invested at 6% and $2800 at 9%.

I hope this helps.

Abe