Answer:
$3400 was loaned out at 8% and $9600 was loaned out at 18%
Step-by-step explanation:
Let Amount loaned out at 8%=$A
Let Amount loaned out at 18%=$B
Total Amount Loaned = $13,000
A + B = 13000 .....(i)
Simple Interest = [tex]\frac{Principal X Rate X Time}{100}[/tex]
Interest on A=[tex]\frac{A X 8 X 1}{100}=\frac{8A}{100}[/tex]
interest on B=[tex]\frac{ BX 18 X 1}{100}=\frac{18B}{100}[/tex]
Total Interest = [tex]\frac{8A}{100}+\frac{18B}{100}=\frac{8A+18B}{100}[/tex]
So,[tex]\frac{8A+18B}{100}=2000[/tex] i.e. [tex]8A+18B=200000[/tex]......(ii)
Next we solve the two equations simultaneously
A + B = 13000 .....(i)
[tex]8A+18B=200000[/tex] ......(ii)
From (i) A=13000-B
Substituting into (ii)
8(13000-B)+18B=200000
104000-8B+18B=200000
10B=200000-104000=96000
B=9600
Recall A + B = 13000
A + 9600 = 13000
A=13000-9600=3400
Therefore: A= $3400 and B=$9600