SOLUTION: Carmel put $5000 into 3 different accounts at paid interest of 8%, 10%, and 7% . Total itnerest at the end was $405. If carmel invested 500$ more at 10% than at 8%, find amount inv

Question 271481: Carmel put $5000 into 3 different accounts at paid interest of 8%, 10%, and 7% . Total itnerest at the end was $405. If carmel invested 500$ more at 10% than at 8%, find amount invested in each.
Set it up in a 3 variable system to find.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Carmel put $5000 into 3 different Carmel put $5000 into 3 different accounts at paid interest of 8%, 10%, and 7% . Total itnerest at the end was $405. If carmel invested 500$ more at 10% than at 8%, find amount invested in each.
If carmel invested 500$ more at 10% than at 8%, find amount invested in each.
;
Let x = amt at 8%
Let y = amt at 10%
Let z = amt at 7%
:
Write an equation for each statement
:
"Carmel put $5000 into 3 different accounts".
x + y + z = 5000
:
"Total interest at the end was $405."
.08x + .10y + .07z = 405
;
"invested 500$ more at 10% than at 8%,"
y = x + 500
:
Replace y with (x+500) in the first equation
x + (x+500) + z = 5000
2x + z = 5000 - 500
2x + z = 4500
z = (4500 - 2x); we can use this for substitution later
:
do the same in the 2nd equation
.08x + .10(x+500) + .07z = 405
.08x + .10x + 50 + .07z = 405
.18x + .07z = 405 - 50
.18x + .07z = 355
:
Replace z with (4500-2x) in the above equation
.18x + .07(4500 - 2x) = 355
.18x + 315 - .14x = 355
.18x - .14x = 355 - 315
.04x = 40
x =
x = $1000 invested at 8%
:
z = 4500 - 2(1000)
z = $2500 invested at 7%
:
y = 1000 + 500
y = $1500 invested at 10%
;
:
I'll let you check solution by finding the total interest
.08(1000) + .10(1500) + .07(2500) =
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