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#1 2021-11-30 09:50:45

Hannibal lecter
Registered: 2016-02-11
Posts: 330

monthly waste collection charge

government charge  $8 for each 32 gallon and $12.32 for 68 gallon how to calculate the dollar for each 1 galloon
I understand it's =
(12.32−8)/(68 − 32) = 0.12 dollars per gallon but can you please illustrate that how? because if I didn't find the answer of that I wouldn't solve it myself never, don't talk to me about slope and linear equations please, what is the relationship between the government charge $8 for each 32 gallon and the government charge 12.32$ for 68 galloon how could the book determine the dollar per galloon like that
because before I see the solution ... I did that ( don't laugh I know it's silly but I want you to check how I solve it) :
I simply divide 8/32 = 0.25 dollar each gallon

Last edited by Hannibal lecter (2021-11-30 09:58:41)

Wisdom is a tree which grows in the heart and fruits on the tongue


#2 2021-11-30 21:14:37

Registered: 2010-06-20
Posts: 9,358

Re: monthly waste collection charge

hi Hannibal lecter

It's hard to say, without more information, exactly how these charges are determined.  My best guess would be that there are two components in the charge (1) a fixed call out charge to cover the cost of travel to the pick up point; and (2) a charge based on how much waste there is.

So I thought I would start by plotting the two points (amount of waste on the x axis, charge on the y axis)


I've assumed that there is a straight line connection between the points.  There are many other possibilities which is why more information is needed. For example the cost might be a fixed charge up to a certain amount; then a step up to a new higher rate.

If the straight line is correct, then you can see that even when no waste is collected (x=0 on the graph) there is still a cost (just over $4).  This would be the fixed cost of travel amount.  Then, as the amount of waste goes up the cost goes up steadily.

If you do 8/32 you get the cost of waste charge as if there is no fixed cost.  The graph for that would go through (0,0) and (8,32).  That line wouldn't go through (68,12.32) so we know that interpretation isn't correct.  If you do 12.32/68 you get a different answer.

There is an equation for working out the charge for any amount of waste, but the employee who sends out the invoices could just use the graph to determine how much to charge.  Say a customer has 50 gallons of waste; go to 50 on the x axis; go straight up to the line; look at the y coordinate there (just over $10).

If the charge is a step function then there would be a charge table that might look like this:

waste in gallons            charge in $

0 - 5                                20
5-10                                32
10-20                              40


Of course I've just made these up. I've no idea what the real table would look like.


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