Question

Charles Miller invested his textbook royalty income in two accounts, one paying 3% annual simple interest and the other paying 2% interest. He earned a total of $11 interest. If he invested three times as much in the 3% account as he did in the 2% account how much did he invest at each rate

Answer 1

The amount invested at 3% is 300 &

The amount invested at 2% is 100.

Explanation:

Total yearly interest for the two accounts is: $11

Let x be the amount invested at 3%

& y be the amount invested at 2%

From the question we can get 2 equations as;

x = 3y --------------------------Equation 1

0.03x + 0.02y = 11 ----------Equation 2

Substitute for x in Equation 2 we get;

0.03 (3y) + 0.02y = 11

0.09y + 0.02y = 11

0.11y = 11

Divide the above equation by 0.11, we get;

y =
`(11)/(0.11)`

y = 100

Let us substitute the value of y in Equation 1 we get;

x = 3(100)

x = 300

Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:

0.03 x 300 + 0.02 x 100

= 9 + 2

= 11

Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.