Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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
share|improve this question
    
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
add comment

2 Answers

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

share|improve this answer
    
You should add the homework tag to explicit homework problems. (Have done so now.) –  Assad Ebrahim Sep 10 '12 at 2:10
    
@AKE. Thanks for doing so. –  Shankara Pailoor Sep 10 '12 at 2:17
    
From that equation, y= -23,529.4. That seems incorrect given the context? –  Faeynrir Sep 10 '12 at 2:20
    
I get $y = 100,000$ –  Shankara Pailoor Sep 10 '12 at 2:26
add comment

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:

$0.09x + 0.10y + 0.12z = 52000$
$x+y+z = 500000$
$y = 2.5x$

share|improve this answer
    
Sorry for my ignorance, how would I set up the matrix from these equations? I'm not sure how to handle the third one in the context of the other two equations. –  Faeynrir Sep 10 '12 at 3:37
    
Totally unrelated (I can't comment on a deleted post) : you may want to have a look at this chat message about some french. –  Nikana Reklawyks Nov 13 '12 at 8:35
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.