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Question

Mr. Jackson borrowed money from his bank and on his life insurance to start a business. His interest rate on the bank loan was 10%, and his rate on the insurance loan was 14%. If the total amount borrowed was $100,000 and his total yearly interest payment was $12,200, how much did he borrow from the bank?

 

if you could show me step my step how to do this, it would be great help. 

Answer 1

Let X be the amount borrowed from the bank and Y be the amount borrowed from the life insurance.

 

 X + Y = 100000 <---- he borrowed $100k

 

0.10X + 0.14Y = 12200 <--- 10% = 0.10 and 14% = 0.14; The total interest is $12.2 k

 

Solving the first equation for Y and multiplying the second equation by 100 to clear the decimals:

 

 Y  = 100000 - X

 

10X + 14Y = 1220000

 

Plugging the first equation into the second:

 

10X + 14( 100000 - X) = 1220000

 

10X + 1400000 - 14X = 1220000  <---- distributive property

 

 

0 = 14X - 10X + 1220000 - 1400000  <--- moves everything to right side, signs change; like to keep coefficient positive

 

0 = 4X -180000  <--- combines like terms

 

180000 = 4x <---- solves for X

 

180000/4 = X <--- adds 180000 to both sides; then divides by 4

 

X = 45000

 

Y = 100000 - 45000 = 55000

 

CHECK:  45000 x 10% + 55000 x 14% = 45000 x 0.10 + 55000 x 0.14 = 12200

 

He borrowed 45000 from the bank and 55000 from the insurance.

The answers are checked, verified, and proven to be correct