Question 288233
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%.