SOLUTION: Hi, Here's another GRE math test prep word problem that has me stumped. I can't find the right equation to use. Pat invested a total of $3,000. Part of the money yields 10% inter

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Question 170449: Hi,
Here's another GRE math test prep word problem that has me stumped. I can't find the right equation to use.
Pat invested a total of $3,000. Part of the money yields 10% interest, and the rest yields 8% interest per year. If the total yearly interest from this investment is $256, how much did Pat invest at 10% and how much at 8%?
Thanks,
Julie
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
remember how you would do this if you had the amounts he invested at 8% and 10%
:
interest earned in one year would be the amount invested times the interest rate. In this case we must break apart the total amount invested in to two different amounts with 2 different interest rates but we do know the total which is $3000. so lets call one amount(amount invested at 8%) x which would make the other amount(invested at 10%) 3000-x. Now we have what it takes to set this problem up
:
8%x+10%(3000-x)=256---->change % to decimal form
:
.08x+.10(3000-x)=256----->distribute
:
.08x+300-.1x=256--->combine like terms
:
.02x=44
:
highlight%28x=2200%29dollars invested at 8%
highlight%283000-2200=800%29dollars invested at 10%