Question 468996: shipping charges at an online bookstore are $4 for one book, $6 for two books and $7 for three to five books. last week, there were 6400 orders of five or fewer books, and a total shipping charges for these orders was $33,600. the number of shipments with $7 charges was 1000 less than the number with $6 charges. how many shipments were made in each category (one book, two books and three to five books)?
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! Let A,B,C be number of shipments for 1-book,2-book,3-book respectively
The cost of those shipments is 4A, 6B, and 7C respectively
Given is total number of shipments, total cost, and the fact that C is 1000 less than B.
Now set up equations:
A + B + C = 6400
4A + 6B + 7C = 33,600
C = B - 1000
Substitute (B-1000) for C in first 2 equations
A + B + (B-1000) = 6400
4A + 6B + 7(B-1000) = 33,600
Combine like terms
A + 2B = 7400
4A + 13B = 40,600
Now solve for A or B using elimination or substitution method
I prefer elimination in this case
Multiply top equation by -4, this will eliminate the A's
-4A - 8B = -29,600
4A + 13B = 40,600
Add equations
5B = 11,000
Divide by 5 on both sides
B = 2200
Find C by subtracting 1000
C = 1200
Find A by subtracting B and C from 6400
A = 3000
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