Greenfield Manufacturing borrowed 30000 to buy a new piece o

Greenfield Manufacturing borrowed $30,000 to buy a new piece of equipment. Part of the money was borrowed at 8%, part at 10%, and part at 12%. The annual interest was $3040, and the total amount borrowed at 8% and 10% was twice the amount borrowed at 12%. How much was borrowed at each rate?

*Book Answers- 8%: $8,000, 10%: $12,000, 12%: $10,000*

Solution

Let amount borrowed at 8% be z, at 10% be y and at 12% be x.

Then, according to the question:

z+y+x = 30,000

and y+z = 2x

Solving above two, we get:

2x + x = 30,000

This implies: x = $ 10,000

and y + z = 20,000 ------------------------------------------(1)

Also, annual interest is $ 3040, we get:

12x/100 + 10y/100 + 8z/100 = 3040

Put x = $ 10,000 in above question, we get:-

12*10,000/100 + 10y/100 + 8z/100 = 3040

10y/100 + 8z/100 = 1840 ------------------------------------(2)

Solving equation (1) and (2), we get:

10y/100 + 8*(20,000 - y)/100 = 1840

2y/100 = 1840 - 1600

y = $ 12,000

and we know, y + z = 20,000

This implies, z = $ 8,000

Therefore, sum borrowed at 8% was $8,000.

Sum borrowed at 10% was $ 12,000.

Sum borrowed at 12% was $ 10,000.

Hence proved and it matches with the Book answers given by you as well.