Question

A bank loaned out $30,000, part of it at the rate of 15% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $3,550.00. How much was loaned at each rate?

Answer 1

x represent the value loaned at 15% and y represent the value loaned at 10%.

`x=11000` and
`y=19000`

Explanation:

We are going to write a system of two linear equations. The first equation will represent the total amount loaned.

`x+y=30000`

Now the second equation are will represent the interest earned for both loans.

`(x*0.15)+(y*0.10)=3550`

Then x represent the value loaned at 15% and y represent the value loaned at 10%. Now solving the equation system we have:

`x=30000-y` using this in the other equation to find y

`((30000-y)0.15)+(0.10*y)=3550`

`4500-0.15y+0.10y=3550`

`4500-0.05y=3550`

`4500-3550=0.05y`

`950=0.05y`

`(950)/(0.05)=y`

`19000=y`

With the value of y we can find x

`x=30000-19000`

`x=11000`