interest problem

Question

Adam sold a sports car that he restored for $48,000. He paid 28% of this amount to the
body shop that did some of the custom work. The balance was invested in two ways,
some of it at 3.25% interest and some at 1.75% interest. The investments produced
$904.80 interest per year. Find the amount invested at each rate.

Answer 1

Let x = the amount invested at 3.25% and y = the amount invested at 1.75%. Assume annual compounding.

 

The amount which was invested in both accounts is

 

48000 · (1 - 0.28) = $34560.

 

Once you have this, you can form a SYSTEM of two equations in x and y:

 

x + y = 34560

 

.0325 x + .0175 y = 904.80

 

The best way to solve this is to clear the decimals in he second equation by multiplying both sides by 400:

 

13x + 7y = 361920.

 

(I got 400 by finding the LCD of the two decimals after converting them to fractions: .0325 = 13/400 and .0175 = 7/400.)

 

The next steps are up to you. You can use substitution or elimination, but I recommend substitution because of the size of the numbers.

 

Good luck!