Question

An actor invests some money at 9​% simple​ interest, and ​$24,000 more than three times the amount at 10​% simple interest. The total annual interest earned from the investment is ​$38,670. How much did he invest at each​ amount? Use the​ six-step method.

Answer 1

Answer:

The amount invested at 9% is $93000

The amount invested at 10% is $303000

Step-by-step explanation:

Let the amount invested at 9% interest rate be x

And the amount invested at 10% rate be y

Simple Interest from x in a year = 0.09x

Simple Interest from y in a year = 0.1y

But y = 24000 + 3x

And the sun of the interests, 0.09x + 0.1y = 38670

Now we have a simultaneous eqn

y = 24000 + 3x (eqn 1)

0.09x + 0.1y = 38670 (eqn)

Substitute y into eqn 2

0.09x + 0.1(24000 + 3x) = 38670

0.09x + 2400 + 0.3x = 38670

0.39x = 38670 - 2400

x = 36270/0.39 = $93000

y = 24000 + 3x = 24000 + 3 × 93000 = $303000