Applications: Interest and Mixtures

Question

James invested some money at 7% interest. James also invested $97 more than 2 times that amount at 5%. How much is invested at each rate if James receives $315.61 in interest after one year? (Round to two decimal places if necessary.)

 

what amount is invested at 7% ______________

 

what amount is invested at 5%_____________

Answer 1

We know that the interest at 7% is equal to .07(x) where x is the amount invested at 7%.  The interest earned at 5% is equal to .05(2x+97).  We know these 2 quantities combined is equal to 315.61, so we can formulate the equation

 

.07x+.05(2x+97)=315.61

.07x+.1x+4.85=315.61

.17x+4.85=315.61

.17x=310.76

x=1828

 

so he invests 1828$ at 7% and

he invests 2(1828)+97 = 3753$ at 5%

 

we can check this with .07(1828)+.05(3753) = 315.61