Applications: Interest & Mixture

Question

James invested some money at 15% interest.  James also invested $229 more than 4 times that amount at 6%.  How much is invested at each rate if James receives $1452.84 interest after 1 year? (Round to two decimal places if necessary.)

Answer 1

Identify unknown (x).

james invested "some money" (x) at 15% interest =.15x

james also invested $229 more (add 229) than 4 times (multiply by 4) that amount(x) at 6%= .06(4x+229)

total interest from both accounts after 1 year=1452.84

 

.06(4x+229)+.15x=1452.84

solve for x to find amount invested at 15%

Plug in value of x to find amount invested at 6% = 4x+229

Answer 2

Let x = the amount James invested at 15%.  The amount he invested at 6% is 4x+229.

 

Interest = Amount*Rate*Time

 

Interest = Interest at 15% + Interest at 6%

 

1452.84 = x*(0.15)*(1 year) + (4x+229)*(0.06)*(1 year)

 

1452.84 = (0.15)x + (.24)x + 13.74

 

$1439.10 = (0.39)x

 

Solve for x, the amount of $ invested at 15%.  Once you have the value of x, the amount invested at 6% is 4x+229.