SOLUTION: Eleanor invests $18,000 in two funds paying 9 1/4% and 10 1/2% simple interest. How much is invested at each rate if the total yearly interest is $1827.50?

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Question 165655: Eleanor invests $18,000 in two funds paying 9 1/4% and 10 1/2% simple interest. How much is invested at each rate if the total yearly interest is $1827.50?
Found 2 solutions by jojo14344, stanbon:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Let x =amount invt. @ 10-1/2%
So, 18000-x = amount invt. @ 9-1/4%
Showing into eqn. with simple interest:
0.105%28x%29%2B0.0925%2818000-x%29=1827.50
0.105x%2B1665-0.0925x=1827.50
0.0125x=1827.50-1665=162.50
cross%280.0125%29x%2Fcross%280.0125%29=cross%28162.50%2913000%2Fcross%280.0125%29
x=13000 -----------------> amount invt. @ 10-1/2%
18000-13000=5000 --------> amount invt. @ 9-1/4%
It make sense to invest more at higher interest I guess.
Check,
0.105%2813000%29%2B0.0925%285000%29=1827.50
1365%2B462.50=1827.50
1827.50=1827.50
Thank you,
Jojo

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Eleanor invests $18,000 in two funds paying 9 1/4% and 10 1/2% simple interest. How much is invested at each rate if the total yearly interest is $1827.50?
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EQUATION:
interest + interest = interest
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0.0925x + 0.105(18000-x) = 1827.50
Multiply thru by 10000 to get:
925x + 1050(18000-x) = 18275000
-125x = 18275000 - 1050*18000
-125x = -625000
x = $5000 (Amt. invested at 9 1/4 %
18000-x = $13000 (Amt. invested at 10 1/2 %
=============================================
Cheers,
Stan H.