Algebra Help

Question

The total annual interest from 2 investments is 81$. Some amount of money is invested at 5% simple interest and $300 more than this amount is invested at 7% simple interest. How much was invested at each rate?

Answer 1

So let's call the capital of the first investment at 5%, P. Let's call the capital of the 7% investment Q.

 

But note that Q = P+$300. We will substitute in this expression for Q, so that we can get our equations all in one term (P).

 

Thus 0.05*P + 0.07*Q = $81 = 0.05 * P + 0.07 (P+$300)

 

0.05 * P + 0.07 * (P+$300)= 0.12 * P + $21 = $81

 

Thus 0.12 * P = $60

Thus P = $60 / 0.12 = $500.00

Thus Q = $800.00

 

We can check our answers by  noting that 0.05 * $500.00 + 0.07 * $800.00 = $81