Question

A bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $1,940.00. How much was loaned at each rate?
___was loaned at 12% and
___was loaned at 10%

Answer 1

Answer: $9500 was loaned at 12% and $8000 was loaned at 10%

Step-by-step explanation:

Let x represent the amount that the

bank loaned out at the annual rate of 12%.

Let y represent the amount that the

bank loaned out at the annual rate of 10%.

The bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest.. It means that

x + y = 17500

The interest on $x after 1 year would be

12/100 × x = 0.12x

The interest on $y after 1 year would be

10/100 × y = 0.1y

The total interest earned for both loans was $1,940.00. . It means that

0.12x + 0.1y = 1940- - - - - - - - - 1

Substituting x = 17500 - y into equation 1, it becomes

0.12(17500 - y) + 0.1y = 1940

2100 - 0.12y + 0.1y = 1940

- 0.12y + 0.1y = 1940 - 2100

- 0.02y = - 160

y = - 160/ - 0.02

y = 8000

x = 17500 - y = 17500 - 8000

x = $9500