SOLUTION: PROBLEM: A bank loaned out $12,000, part of it at a rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was loaned at 8%?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: PROBLEM: A bank loaned out $12,000, part of it at a rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was loaned at 8%?      Log On


   

Question 10496: PROBLEM: A bank loaned out $12,000, part of it at a rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was loaned at 8%?

Ok I know that it should be set up with the I=prt formula. After that I'm not sure where to go. The book gives me the answer ($11,600 at 8%) but I need to know how to get that answer! Please help! Thanks!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You don't really need the I = prt formula to solve this problem.
Try this:
Let x = amount loaned at 8% and ($12,000 - x) = amount loaned at 18%
Write the equation: (change the percents to decimals: 8% = 0.08 and 18% = 0.18)
(0.08)x + (0.18)($12,000 - x) = $1,000
This expresses the total amount of earned interest in terms of the amounts of the loan, x and ($12,000 - x}.
0.08x + $2,160 - 0.18x = $1,000 Simplify and solve for x.
-0.1x = -$1,160 Divide both sides by -0.1
x = $11.600 The amount loaned at 8% interest.