small corporation borrowed $1,500,000

Question

small corporation borrowed $1,500,000 To expand their business. Some was borrowed at 7%, some at 8% and some at 10% for a total of 130,500 and interest. The amount borrowed at 10% was four times the amount borrowed at 7%. solve for how much was borrowed at each percentage.

Answer 1

Let x be the amount borrowed at 7% and y be the amount borrowed at 8% and z be the amount borrowed at 10%.

x+y+z = 1500000 (Eq1)

z = 4x (Eq2)

0.07x + 0.08y + 0.10 z = 130500 (I think it should of read 130,500 in interest)

We can multiply the last equation by 100 so that we can stay with integers.

7x + 8y + z = 13050000 (Eq3)

Substitute 4x for z in Eq1 and Eq3

x+y+4x = 1,500,000

7x+8y+40x = 13,050,000

5x + y = 1,500,000 --> y = 1,500,000-5x

47x + 8y = 13,050,000 (Eq5)

substitute for y in Eq5.

47x + 8(1,500,000-5x) = 13,050,000

47x+12,000,000-40x = 13,050,000

7x = 1,050,000

x = 150,000

z = 4x = 600,000

y = 1,500,000 - 600,000 - 150,000 = 750,000

The company borrowed $150,000 at 7% and $750,000 at 8% and $600,000 at 10%

Answer 2