# Need Homework Help: A small corportion borrowed $500,000, some at 9%, 10% and 12%. Use a system of equations--how much was borrowed at each rate if… A small software corporation borrowed 500,000 cash 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$52,000 and the amount borrowed at 10% was 2.5 times the amount borrowed 9%.

I have no idea where to start with this problem. Can I get some help?

Thank you very much.

Here's what I have so far:

0.09x + 0.1y + 0.12z = ?

2.5x = y

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Was all the 500,000 borrowed at each of the interest rates? I.e, some at 9%, some at 10% and the rest at 12%? – Shankara Pailoor Sep 10 '12 at 1:53
Yes, all was borrowed at each, respectively. – Faeynrir Sep 10 '12 at 5:07

Let $x$ be the amount borrowed at $10$% and let $y$ be the amount borrowed at $9$%. We know the amount borrowed at $12$% is $500,000 - (x+y)$ . Since the amount borrowed at $10$% is 2.5 times the amount borrowed at $9$% we have that $2.5y = x$. Now $$1.12(500,000 - 3.5y) + 1.1(2.5y) + 1.09y - 500,000 = 52,000.$$ The amount $1.12(500,000 - 3.5y) + 1.1(2.5y) + 1.09y$ gives us the money we borrowed plus interest. That is why we subtract the $500,000$.
Try solving for $y$. Once you have solved for $y$ you can find $x$ because $x = 2.5y$. Once you know those two you can easily find out how much is borrowed at $12$%. If you have further trouble let me know
I get $y = 100,000$ – Shankara Pailoor Sep 10 '12 at 2:26
A small software corporation borrowed 500,000 cash 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 $52,000 and the amount borrowed at 10% was 2.5 times the amount borrowed 9%. Let$x$= Amount borrowed at 9% Let$y$= Amount borrowed at 10% Let$y$= Amount borrowed at 12% The equations are:$0.09x + 0.10y + 0.12z = 52000x+y+z = 500000y = 2.5x\$