# 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?

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 Click here to see ALL problems on Probability-and-statistics 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%.