SOLUTION: A bank loans me $13,000 for one year. Part of the loan is at 8% Part of the loan is at 18% The total interest paid is $2,000. How much of the $2,000 was at 8% and how much was

Question 407744: A bank loans me $13,000 for one year.
Part of the loan is at 8%
Part of the loan is at 18%
The total interest paid is $2,000.
How much of the $2,000 was at 8% and how much was at 18%
And how do I solve for that?
Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bank loans me $13,000 for one year.
Part of the loan is at 8%
Part of the loan is at 18%
The total interest paid is $2,000.
How much of the $2,000 was at 8% and how much was at 18%
:
We can solve it using two unknowns
Let a = amt of loan at 8%
Let b - amt of loan at 18%
:
Write an equation for the total amt
a + b = 13000
a = (13000-b); use this form for substitution
:
Write an equation for the total interest:
.08a + .18b = 2000
:
Replace a with (13000-b)
.08(13000-b) + .18b = 2000
1040 - .08b + .18b = 2000
-.08b + .18b = 2000 -1040
.10b = 960
b =
b = $9600 at 18% interest
and
13000-9600 = $3400 at 8% interest
:
:
You can check these solutions in the total interest equation
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