Question

An actor invests some money at 99​%, and 45000 more than four timesfour times the amount at 12%. The total annual interest earned from the investment is ​$65250. How much did he invest at each​ amount? Use the​ six-step method.

Answer 1

Answer:

$ 40714.28 at 99% and $ 207857.14 at 12%

Explanation:

Let the amount invested at 99% be 'x' and the amount invested at 12% be 'y'

Given:

y = 4x + 45000   .............(1)

thus,

the interest earned from x = 99% of x = 0.99x

and the interest earned from y = 12% of y = 0.12y

also

0.99x + 0.12y = $ 65250  ...............(2)

substituting the y from the 1 in the equation 2, we get

0.99x + 0.12× (4x + 45000) = $ 65250

or

0.99x + 0.48x + 5,400 = $ 65,250

or

1.47x = $ 59,850

or

x = $ 40714.28

and y = 4x + 45000

or

y =  4 × (40714.28) + 45000

or

y = $ 207857.14