# Thread: in a hurry...thanks

1. ## in a hurry...thanks

Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $72, while one using 1600 cubic feet was billed$108.

(a) What is the exact charge per cubic foot?

(b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used.

(c) How many cubic feet of water used would lead to a bill of $135? Give your answer to the nearest cubic foot. ok, i just need some help with this problem....last time i did it, it didn't seem to work right...any help is greatly appreciated...thanks mathlete 2. Originally Posted by mathlete Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed$72, while one using 1600 cubic feet was billed $108. (a) What is the exact charge per cubic foot? (b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used. (c) How many cubic feet of water used would lead to a bill of$135? Give your answer to the nearest cubic foot.

ok, i just need some help with this problem....last time i did it, it didn't seem to work right...any help is greatly appreciated...thanks

mathlete
it seems obvious that there is a linear relationship here between the charge and the amount of water used.

so start with $C = mw + b$

where $C$ is the charge, $m$ is the slope (the charge per cubic foot of water used), and $b$ is the y-intercept (the fixed charge), and $w$ is the amount of water used in cubic feet

now we need to find $m$ and $b$. once we have those, we can answer the questions.

we are given two points on this line: $(w_1,C_1) = (1000, 72)$ and $(w_2,C_2) = (1600, 108)$

we can use these two points to find the slope, and then use that to find the y-intercept

3. Originally Posted by Jhevon
it seems obvious that there is a linear relationship here between the charge and the amount of water used.

so start with $C = mw + b$

where $C$ is the charge, $m$ is the slope (the charge per cubic foot of water used), and $b$ is the y-intercept (the fixed charge), and $w$ is the amount of water used in cubic feet

now we need to find $m$ and $b$. once we have those, we can answer the questions.

we are given two points on this line: $(w_1,C_1) = (1000, 72)$ and $(w_2,C_2) = (1600, 108)$

we can use these two points to find the slope, and then use that to find the y-intercept

ok i got b and c, can you give me more on how to find the exact charge per cubic feet

4. Originally Posted by mathlete
ok i got b and c, can you give me more on how to find the exact charge per cubic feet
the exact charge per cubic foot is m

(you're not supposed to be finding C, C i sthe output. we leave it as a variable