SOLUTION: Barneys money earned $204 in interest after 1 year. He invested some of is money in an account earning 6% simple interest and $450 more than that account earning 5% simple interest

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Question 910909: Barneys money earned $204 in interest after 1 year. He invested some of is money in an account earning 6% simple interest and $450 more than that account earning 5% simple interest. Find the amount Barney invested in each account.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
This plan has more at 5%
We don't know the total invested.
We know the difference in the two accounts.
We know that the interest for the two accounts is $204
0.05*x+0.06*y=204
We know that the account at 5% has $450 more.
x=450+y
We substitute for x
0.05*(450+y)+0.06*y=204
We multiply out
22.5+0.05y+0.06*y=204
We combine like terms.
0.11*y=181.5
Isolate y
y=$1650 at 6%
x=450+y
Calculate x
x=$2100 at 5%
Now,we know the total invested is: 3750
Total invested $2100+$1650=$3750
We check
0.05*2100+0.06*1650=204
105+99=204
204=204
Since this statement is TRUE and neither x nor y is negative all is well.
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