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:
 \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.
