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Question 1048386: Marina had RM24,500 to invest. She divided the money into three different accounts. At the end of the year, she had made RM1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Marina had RM24,500 to invest.
She divided the money into three different accounts.
At the end of the year, she had made RM1,300 in interest.
The annual yield on each of the three accounts was 4%, 5.5%, and 6%.
If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?
:
let a = amt in the 4% acct
let b = amt in the 5.5% acct
let c = amt in the 6%
:
"Marina had RM 24,500 to invest."
a + b + c = 24500
" At the end of the year, she had made RM1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%."
.04a + .055b + .06c = 1300
"If the amount of money in the 4% account was four times the amount of money in the 5.5% account,"
a = 4b
how much had she placed in each account?
:
Replace a with 4b in both equations, simplify
4b + b + c = 24500
5b + c = 24500
c = -5b + 24500
:
.04(4b) + .055b + .06c = 1300
.16a + .055b + .06c = 1300
.215b + .06c = 1300
replace c with (-5b+24500)
.215b + .06(-5b+2400) = 1300
.215b - .3b + 1470 = 1300
-.085b = 1300 - 1470
b = -170/-.085
b = $2000 in the 5.5% investment
then
c = -5(2000) + 24500
c = -10000 + 24500
c = $14,500 in the 6%
Find a using the 1st equation, replace b & c
a + 2000 + 14500 = 24500
a = 24500 - 16500
a = $8000 in the 4% acct
:
:
You can check this in the 2nd equation
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