Question

George invested some money at10% interest. George also invested$169 more than4 times that amount at15 % . How much is invested at each rate if George receives$2427.05 in interest after one year? (Round to two decimal places if necessary.)

Answer 1

The investment is in two places. The first one had a principal of P, with an interest rate of 10% (that is 0.10). The second one had a principal of 169 more than 4 times the first one, which can be translated as;

4P + 169. The interest rate is 15% (that is 0.15)

So, investment X is;

Interest x = PRT

Interest x = P*0.1*1

Interest x = 0.1P

Investment Y is;

Interest y = PRT

Interest y = (4P + 169)*0.15*1

Interest y = 0.6P + 25.35

This means the total interest yielded is given as;

Interest x + interest y = 0.1P + 0.6P + 25.35

Interest x + interest y = 0.7P + 25.35

If however, he receives 2427.05 in interest, then this can be translated as follows;

`\begin{gathered} \text{Interest x+interest y=0.7P+25.35} \\ \text{Similarly;} \\ \text{Interest x+ interest y=2427.05.} \\ \text{Therefore;} \\ 0.7P+25.35=2427.05 \\ 0.7P=2427.05-25.35 \\ 0.7P=2401.7 \\ P=(2401.7)/(0.7) \\ P=3431 \end{gathered}`

With P calculated as 3,431, this can be translated as follows;

Investment X had a principal of $3,431. The interest rate was 0.10 and that yielded an interest after a year in the sum of 343.10.

Investment Y had a principal of 4P + 169 which equals;

4 (3431) + 169 = 13,893

And the interest rate was 0.15, which now yielded an interest after a year of 2,083.95.

Therefore, Investment X was $3431 at 10%

Investment Y was $13,893 at 15%