SOLUTION: A bank loaned out $120,000, part of it at the rate of 8% annual mortgage interest and the rest at the rate of 18% annual credit card interest. The interest received on both loans

Question 87051This question is from textbook Intoductory Algebra
: A bank loaned out $120,000, part of it at the rate of 8% annual mortgage interest and the rest at the rate of 18% annual credit card interest. The interest received on both loans totaled $10,000. How much was loaned at each rate?
I've tried calculating this and I can't make it work within the $10,000 interest amount. I keep coming up with more interest than this. The problem is from a worksheet handed out my the instructor and is not in my textbook. This question is from textbook Intoductory Algebra

Answer by rossiv53(27) (Show Source): You can put this solution on YOUR website!
Since the bank lent out two amounts, substitute x for one of the amounts. It doesn't matter which one. First amount is x and second amount is (120,000-x).
We know that the principal multiplied by the rate of interest will give us the interest. First amount is x multipied by 8% or .08. That interest is equal to .08x. Second amount is (120,000-x) multiplied by 18% or .18. That interest is equal to .18(120,000-x). Since you know that the interest from both amounts is equal to 10,000, you can set up your equation as
.08x+.18(120,000-x)=10,000 then solve for x.
.08x + 21600-.18x=10000
-.10x+21600=10000
-.10x+21600-21600=10000-21600
-.10x=-11600
x=116,000
Second equation is 120,000-116,000. That is equal to 4,000.
So, 116,000 was lent at 8% and 4000 at 18%. The combined interest from these amounts equals 10,000.

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