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

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.

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.

Your three equations are

x+ y+ z= 384,

8x+ 6y+ 4z= 2160, and

-2x+ 0y+ z= 12.