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A small software corporation borrowed $ 250,(000) to expand its software line. The corporation borrowed some of the money at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest rate was $26,000 and the amount borrowed at 10% was 2.5 times the amount borrowed at 9%.

Respuesta :

Answer:

$50,000 was borrowed at 9%.

$125,000 was borrowed at 10%.

$75,000 was borrowed at 12%.

Step-by-step explanation:

Let amount borrowed at 9% be x

Let amount borrowed at 10% be y

Let amount borrowed at 12% be z

Now equations form:

[tex]x+y+z=250000[/tex]      ....(1)

[tex]0.09x+0.10y+0.12z=26000[/tex]     ....(2)

[tex]y=2.5x[/tex]   ..... (3)

Substituting the value of y from (3) in (1) and (2)

[tex]x+2.5x+z=250000[/tex]

=> [tex]3.5x+z=250000[/tex]   ......(4)

[tex]0.09x+0.10(2.5x)+0.12z=26000[/tex]

=> [tex]0.34x+0.12z=26000[/tex]   ....(5)

Multiplying (4) by 0.12 and subtracting (5) from it, we get

[tex]0.42x+0.12z=30000[/tex] - [tex]0.34x+0.12z=26000[/tex]

[tex]0.42x-0.34x=30000-26000[/tex]

0.08x=4000

x = $50000

As y = 2.5x

So, [tex]y=2.5\times50000=125000[/tex]

y = $125000

And as x+y+z=250000

=>[tex]z=250000-50000-125000[/tex]

z = $75000

Therefore, $50,000 was borrowed at 9%.

$125,000 was borrowed at 10%.

$75,000 was borrowed at 12%.