SOLUTION: Please help me with this interest problem, I'm not sure what system of equations to write for it. "Half of Roberta’s money is invested at 12% interest, one third of her money i

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Question 1119238: Please help me with this interest problem, I'm not sure what system of equations to write for it.
"Half of Roberta’s money is invested at 12% interest, one third of her money is at 11% and the remainder is invested at 9%. Her total annual income from the investments is 1,340. How much has Roberta invested altogether?"
Thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"Half of Roberta’s money is invested at 12% interest, one third of her money is at 11% and the remainder is invested at 9%.
Her total annual income from the investments is 1,340.
How much has Roberta invested altogether?"
:
let A = total amt invested
Find the remainder fraction, using common denominator, 6
1 - 1%2F2 - 1%2F3
6%2F6 - 3%2F6 - 2%2F6 = 1%2F6
An equation
.12(3%2F6A) + .11(2%2F6A) + .09(1%2F6A) = 1340
Multiply by 6, cancel the denominators
.36A + .22A + .09A = 8040
.67A = 8040
A = 8040/.67
A = $12000 invested
:
You can check this by finding the sum of the actual return on each amt
6000, 4000, 2000