SOLUTION: An actor invests some money at 9%, and $32000 more than twice the amount at 12%. The total annual interest earned from the investment is $23640. How much did he invest at each amou

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Question 176564: An actor invests some money at 9%, and $32000 more than twice the amount at 12%. The total annual interest earned from the investment is $23640. How much did he invest at each amount? Use the six- step method.
Please do this step by step so I can see how you got each number.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ok what we are after is amounts invested at 9% and at 12%. Lets call those x and y respectively
:
We are given that y=2x+32000. So lets write our equation, Lets write it verbally first. (The amount invested) at (x times its interest rate) + (the amount invested) at (y times its interest rate) will give us(equals) the total annual interest earned.
:
so we have
x amount investe at 9%
y=2x+32000...eq 1
:
.09x+.12y=23640...eq 2
:
take y's value from eq 1 and plug it into eq 2
:
.09x+.12(2x+32000)=23640
:
.09x+.24x+3840=23640
:
.33x=19800
:
$highlight%28x=60000%29amount invested at 9%
:
$highlight%28y=2%2860000%29%2B32000=152000%29amount invested at 12%