SOLUTION: Ben invested some money at 8% simple interest and $100 more than this amount at 7%. His total annual interest was $82. How much did he invest at each rate?

Question 288233: Ben invested some money at 8% simple interest and $100 more than this amount at 7%. His total annual interest was $82. How much did he invest at each rate?
Answer by jaydducote(11) (Show Source): You can put this solution on YOUR website!
So the unknown is how much he invested at 8%, so that will be the variable, x.
We know he invested $100 more at 7%, so he invested x+100 at 7%.
Simple interest is not compounded, so we know that since it says "annual" interest, the time period is one year, so he will make exactly 7% and 8% of the amounts. Therefor, we can use the following formula:
.08x+.07(x+100)=82
Make sure you convert 8% to .08 and 7% to .07. Percent means "per 100", so 7% is 7/100, or .07.
distribute the .07 to get:
.08x+.07x+7=82
combine like terms
.15x+7=82
subtract 7 from both sides
.15x=75
divide both sides by .15
x=500
this means that 500 was invested at 8% and (x+100 so 500+100) 600 was invested at 7%.
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