# Systemof linear equations (determinants)- tricky word problem

• Jun 26th 2012, 08:14 AM
aliciambrissette
Systemof linear equations (determinants)- tricky word problem
A mail-order company charges $4 for shipping orders of less than$50, $6 for orders from$50- $200, and$8 for orders over $200. One day the total shipping charges were$2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under $50 is 12 more than twice the number of orders over$200.

I know how to do determinants but just having a hard time figuring out the equations I should be using. Any help would be appreciated. Thank you
• Jun 26th 2012, 11:06 AM
earboth
Re: Systemof linear equations (determinants)- tricky word problem
Quote:

Originally Posted by aliciambrissette
A mail-order company charges $4 for shipping orders of less than$50, $6 for orders from$50- $200, and$8 for orders over $200. One day the total shipping charges were$2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under $50 is 12 more than twice the number of orders over$200.

I know how to do determinants but just having a hard time figuring out the equations I should be using. Any help would be appreciated. Thank you

1. Let x denote the number of the over-200$-orders. Then the less-than-50$-orders are (2x + 12)

and the 50$-to-200$-orders are 384 - (2x + 12) - x = 372 - 3x

2. The shipping costs sum up to:

$\displaystyle \displaystyle{x \cdot 8 + (372 - 3x) \cdot 6 + (2x + 12) \cdot 4 = 2160}$

3. Solve for x.
• Jun 26th 2012, 01:57 PM
HallsofIvy
Re: Systemof linear equations (determinants)- tricky word problem
If you need to do it in terms of matrices and determinants: let x be the number of orders greater than $200, y the number of orders between$50 and $200, and z the number of order less than$50. "A mail-order company charges $4 for shipping orders of less than$50, $6 for orders from$50- $200, and$8 for orders over $200. One day the total shipping charges were$2160"
so 8x+ 6y+ 4z= 2160.

"on 384 orders": x+ y+ z= 384.

"the number of orders under $50 is 12 more than twice the number of orders over$200": z= 2x+ 12.