SOLUTION: A residential water bill is based on a flat fee of $10 plus a charge of $0.75 for each 1000 gal of water used. Find the number of gallons of water a family can use and have a month

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Question 503579: A residential water bill is based on a flat fee of $10 plus a charge of $0.75 for each 1000 gal of water used. Find the number of gallons of water a family can use and have a monthly water bill that is less than $34. Please help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of gallons of water used (in thousands of gallons; so for example, x = 2 means 2 thousand gallons were used). I'm making x be in the thousands because the bill is charging 75 cents per 1000 gallons of water used.


Also, let c = monthly water bill


Since "A residential water bill is based on a flat fee of $10", this means that no matter what, the cost (c) is going to be $10. So if you use no water at all, then c = 10


Mathematically, when x = 0, then c = 10


Now say you use 1000 gallons of water. If you do, then the company will charge you an extra 75 cents on top of the $10 to make the final bill be 10+0.75 = 10.75 dollars. So when x = 1, c = 10.75

Now say you use 2000 gallons of water. If you do, then the company will charge you an extra 2*75 = 150 cents on top of the $10 to make the final bill be 10+2*0.75 = 10 + 1.50 = 11.50 dollars. So when x = 2, c = 11.50

And so on...

So if you use x thousand gallons (where x is some positive integer), then the total cost will be 10+x*0.75 which rearranges to 0.75x + 10


So the cost equation is c = 0.75x + 10

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Now onto the problem:
Find the number of gallons of water a family can use and have a monthly water bill that is less than $34

Since we want the bill (c) to be less than $34, this means that we want c < 34


But c = 0.75x+10, so we can replace 'c' in the inequality above with 0.75x+10 like so

0.75x+10 < 34


Now we solve for x


0.75x+10 < 34

0.75x < 34-10

0.75x < 24

x < 24/(0.75)

x < 32


So the solution is x < 32


Keep in mind that x = number of gallons of water used (in thousands of gallons). Always go back to the definition of each variable when you have a solution.

So x < 32 means that if you use less than 32 thousand gallons of water per month, then the monthly water bill will be less than $34.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim