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%

$9500 was loaned at 12%

$8000 was loaned at 10%.

Step-by-step explanation:

Let x represent the amount which the bank loaned out at the rate of 12% annual interest.

Let y represent the amount which the bank loaned out at the rate of 10% annual interest..

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

x + y = 17500

The formula for determining simple interest is expressed as

I = PRT/100

Considering the amount loaned out the rate of 12% annual interest.

P = $x

T = 1 year

R = 12℅

I = (x × 12 × 1)/100 = 0.12x

Considering the amount loaned out the rate of 10% annual interest,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 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

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step-by-step explanation: