please help with this problem

Question

A bank loaned out $18,000​, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled ​$2500​, how much was loaned at 8 % ?

Answer 1

Let

x=The amount loaned at 8%

y=The amount loaned at 18%

x+y=18000 (1)

So

The interest after 1 year for amount x=0.08x

The interest after 1 year for amount y=0.18y

0.08x+0.18y=2500 (2) or 8x+18y=250000

The variable y is eliminated to get x

8x+18y=250000 (2)

18x+18y=18*18000=324000 (3)

(3)-(1)

10x=74000

x=7400

y=10500

We can verufy that 0.08*7400+0.18*10600=2500 $

All the best !