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#1 2021-12-04 14:09:31

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

my last question this month I know I made you tired from me

I'll provide answers for this question I have the answer but I have a question about the last section
please this question is very necessary for me and it's very silly in the same way

Residents of the town of Maple Grove who are connected
to the municipal water supply are billed a fixed amount
monthly plus a charge for each cubic foot of water used.
A household using 1000 cubic feet was billed $40, while
one using 1600 cubic feet was billed $55.

(a) What is the charge per cubic foot? answer : = $0.025/cu. ft
(b) Write an equation for the total cost of a resident’s Answer : c = b + 0.025w, b = 15, thus : c = 15 + 0.025w,
water as a function of cubic feet of water used.
(c) How many cubic feet of water used would lead to a
bill of $100? Answer of b section is : We need to solve the equation 100 = 15 + 0.025w, which yields w = 3400. It costs $100 to use 3400 cubic feet of
water

the manual solution of section b is confusing me.. I mean I can solve 100 question like that but without understanding it mentally
how to understand this mentally?
he put $100 = $15 + 0.025w
the solution of section a and section b is very easy and I know them
but the last section (b) is confusing me, in which law he put 100 dollar on the left and the other quantity (15 + 0.025w) to find how many cubic feet of water leads to 100$
what is that called in algebra, if you refer me to a link I will open it but I will not understand I need your own answer please if anyone know to to tell me that in easy way

I mean it's interactive math and interactive question, I need interactive answer too not just put 100 and solve the equation and find the cost, I can solve a lot of this question in future but someday I'll forget how to solve it! because I don't have the concepts in my mind and I don't understand this mentally


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

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#2 2021-12-05 01:06:33

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

Re: my last question this month I know I made you tired from me

hi Hannibal lecter

I'm not tired of you yet.  So please don't stop posting for help. But there have been 3  threads where you have posted; Ganesh or me has posted a response; and then nothing.

How are we to know what we have said has actually been helpful?  It would be nice to know and to get some thanks.

If I provide some help and the poster needs more I don't mind if they say that. And it gives me a better idea of where the difficulties are, so I can target my help more effectively.

Now, back to the question.

All your answers are correct.   So what is the difficulty I'm wondering.

If there was no fixed charge then the cost would go up steadily with amount used.

Let's try to imagine how the person who works out the bill actually does it.

They have to do this:

Start with the amount used and multiply by the charge rate. Then add on the fixed amount.

So 1000 times (charge for water used) plus b gives 40 and

     1600 times (charge for water used) plus b gives 55

So the extra 600 seems to have cost $15 more; that's 40 costs $1, or 1 costs $(1/40) or $0.025

So the number in front of the w in the equation is 0.025.

Let's just check so far.

1000 x 0.025 = 25    now add b to get 40  So it looks like b = 15

Check out the second bill.

1600 x 0.025 = 40. Add on the fixed charge which I think is 15 and we get $(40+15) = $55. Correct!

So the method the bill person uses is look up the amount used; multiply by 0.025; add on 15 to get the total in $

Any calculation like this that has a steady rise factor in the charge plus a fixed amount, is called a linear rate.

If you plot (1000,40) and (1600,55) on a graph you can connect them with a straight line (hence the word linear).  It will have a gradient of 0.025 and will cross the c axis at 15. 

The equation is c = 0.025w + 15 where w is the amount used and c is the charge in $.

If you know the charge you can work backwards to get w in that case.  So if c = 100 we have 100 = 0.025w + 15

Take off the fixed charge of 15 and we then have 85 = 0.025w  So 1/40th of w is 85. So w = 40 x 85 = 3400.

Here's some to try:

(1) What is the cost of 2000 cu ft of water?

(2) How much water has been used if the charge is $215 ?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2021-12-05 03:18:51

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

Re: my last question this month I know I made you tired from me

every answers of you is very helpful thank you so much I'm just being reading carefully and in accurate way and slowly and understand it
all of your answers helped me since I'm in the forums but I just don't say "thanks" in a comments because I think you prefer to talk about the subject only no side talk only discussions on the topic that the user posted so I just say thanks inside my mind I said thank you without reply on comments if I didn't understand your answer I'll 100% tell you that in the comment I promise I'm honest


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

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