Question

An actor invests some money at 7​%, and ​$25000 more than twice the amount at 11%. The total annual interest earned from the investment is ​$45670. How much did he invest at each​ amount? Use the​ six-step method.

He invested $ ___ at 7% and $___ at 11%

???HELP

Answer 1

Let
`x_1` be the amount of money invested at 7% and
`x_2` the amount of money invested at 11%. The actor invests
`x_1` at 7% and 25000$ more than
`2x_1` at 11%, it means:

`2x_1+25000=x_2` (Equation 1)
The total annual interest earned is 45670$:

`(7)/(100)x_1+(11)/(100)x_2=45670` (Equation 2).
We remove
`x_2` from equation 2 by using equation 1:

`(7)/(100)x_1+(11)/(100)(2x_1+25000)=45670\\ 7x_1+22x_1+275000 = 4567000\\ 29x_1 = 429200\\ x_1 = 4292000/29 = 148000\\ x_2 = 2x_1+25000 = 321000\\`

He invests 148000$ at 7% and 321000$ at 11%.