SOLUTION: A total of $5,000 was invested, part of it at 5 % interest and the remainder at 7 %. If the total yearly interest amount is $325 , how much was invested at 5 %?

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Question 592081: A total of $5,000 was invested, part of it at 5 % interest and the remainder at 7 %. If the total yearly interest amount is $325 , how much was invested at 5 %?
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Part I 5.00% per annum ---x
part II 7.00% per annum ---y

x+y=5000------------------------1
5.00% x + 7.00% y= 325
Multiply by 100
5x+7y=32500.00 --------2
Multiply (1) by -5
we get
-5x-5y=-25000.00
Add this to (2)
2y=7500
divide by 2
y = 3750 Part I @ 7.00%
Balance 1250 part II @ 5.00%
CHECK
3750 --------- 7.00% ------- 262.50
1250 ------- 5.00% ------- 62.50
Total -------------- 325.00

Answer by josgarithmetic(39790) About Me  (Show Source):
You can put this solution on YOUR website!
RATE%           AMT.             INTEREST
5                x               0.05x
7               5000-x           0.07(5000-x)
                 5000               325

The question asked, "how much invested at 5%?"
The variable is assigned to that amount for that reason.

0.05x%2B0.07%285000-x%29=325
----
0.05x%2B0.07%2A5000-0.07x=325
%280.05-0.07%29x=325-0.07%2A5000
x=%28325-0.07%2A5000%29%2F%280.05-0.07%29
x=%28350-325%29%2F%280.07-0.05%29
x=25%2F0.02
highlight%28highlight%28x=1250%29%29