SOLUTION: Could someone help me with his word problem? Solve by any method and show equations and major steps: Computerwarehouse.com charges $3 for shipping orders up to 10 lb, $5 for or

Question 33715: Could someone help me with his word problem?
Solve by any method and show equations and major steps:
Computerwarehouse.com charges $3 for shipping orders up to 10 lb, $5 for orders from 10 lb to 15 lb, and $7.50 for orders of 15 lb or more. One day shipping charges for 150 orders totaled $680. The number of orders under 10 lb was three times the number of orders weighing 15 lb or more. Find the number of packages shipped at each rate.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
1.) first, define the variables:
s=number of orders under 10 pounds
m=number of orders between 10 and 15 pounds
L=number of orders more than 15 pounds
2.) now, let us produce the three essential equations:
3s + 5m + 7.5L = 680
the cost times the amount of orders will equal the total cost
s - 3L = 0
there were three times as much orders under 10lb than there were above 15lb
s + m + L = 150
there were 150 orders in all
3.) next, you combine equations to get:
5m + 16.5L = 680
and
m + 4L = 150
4.) then, combine these to get:
L = 20
5.) now, plug L into one of the equations mentioned in step (3) and you get:
m = 70
6.) last, plug in m and L in one of the equations mentioned in step (2) and you get: s = 60
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the answer is: s=60 while m=70 while L=20
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