Residents of the town of Maple Grove who are connected to the municipal water su

Question

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 $68, while one using 1600 cubic feet was billed $102. Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used. Use lower case w. How many cubic feet of water used would lead to a bill of $135? (Round your answer to the nearest cubic foot.)

Explanation / Answer

let the the two data relations be taken as two points of x-y coordinate system,
where,
(x1,y1)=>(1000,68)
(x2,y2)=>(1600,102)
therefore y be the bill price i.e. p , and x be the w i.e.,cubic feet of water used.
therefore , we get,
(y-y1)=[(y2-y1)/(x2-x1)]*(x-x1)
=>y-68 = [(102-68)/(1600-1000)]*(x-1000)
=>y-68 = (34/600)*(x-1000)
=>y-68 = (17/300)*(x-1000)
=>x-1000 = (300/17)*(y-68)
=> x = (300/17)*(y-68)+1000
replace x with w and y with p,
=> w = (300/17)*(p-68)+1000
Answer........
w = (300/17)*(p-68)+1000

now,
if p = 135 what's w,
w = (300/17)*(135-68)+1000
= (300/17)*67+1000
= 2182.3529 2182 cubic feet .....Answer...

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