SOLUTION: a bank loaned out $15000, part of it at 8% per year, the rest at 18% per year. if the interest received in one year totaled $2000, how much was loaned at 8%?

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Question 1205334: a bank loaned out $15000, part of it at 8% per year, the rest at 18% per year. if the interest received in one year totaled $2000, how much was loaned at 8%?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Total amount loaned = $15000
x+= total amount loaned at 8%=0.08

y = total amount loaned at18%=+0.18+

so,

x+%2B+y+=+15000....solve for x
x=15000-y.......eq.1

if received in one year totaled 2000 in one year
0.08x+%2B+0.18y+=+2000....eq.2
substitute x
0.08%2815000-y%29+%2B+0.18y+=+2000
1200+-+0.08y%2B+0.18y+=+2000
0.10y+=+2000-1200+
+0.10y+=+800
y=800%2F0.10
y=8000

go to
x=15000-y.......eq.1, substitute y
x=15000-8000
x=7000

answer: $7000+was loaned at 8%

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
15000 total part of it at 0.08 per year, the rest at 0.18 per year.
if received in one year totaled 2000, how much was loaned at 0.08?
~~~~~~~~~~~~~~~~~~~~ 

x at 0.08; the rest, (15000--x), at 0.18.


Write equation for the annual interest

    0.08x + 0.18*(15000-x) = 2000.


Simplify and solve for x

    0.08x + 0.18*15000 - 0.18x = 2000

    0.08x - 0.18x = 2000 - 0.18*15000

      -0.1x       =   -700

          x       = -700/(-0.1) = 70000.


ANSWER.  7000 at 0.08.

Solved.