SOLUTION: $10,000 is invested, part at 4% and the rest at 5% interest. The annual interest from the 4% investment is $40 more than that from the 5% investment. Find the amounts at 4% and 5%

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Question 1151415: $10,000 is invested, part at 4% and the rest at 5% interest. The annual interest from the 4% investment is $40 more than that from the 5% investment. Find the amounts at 4% and 5%
Thanks in advance
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
$10000+is invested, part at 4% and the rest x at 5% interest.
Let
x = amount in dollars invested at 4 %
y = amount in dollars invested at 5 %

x%2By=10000
y=10000-x......eq.1
Convert above information into income.
I=+P%2AR%2AT (Interest = Principal * Rate* Time)
If you put+x in the bank at 4 %=0.04, your interest would be 0.04x
and %2810000-x%29+ at 5 %=0.05, your interest earned from 5% would be 0.05%2810000-x%29+
if the annual interest from the 4% investment is $40 more than that from the 5% investment, we have
0.04x=0.05%2810000-x%29%2B40
0.04x=500-0.05x%2B40
0.04x%2B0.05x=500%2B40
0.09x=540
x=540%2F0.09
x=6000
‭now find y
y=10000-6000 ......eq.1
y=4000

So, $6000 was invested ‬at 4% and $4000 at 5%
check annual interest:
$ 6000%2A0.04=240
$ 4000%2A0.05=200 =>difference is $ 40