Residents of the town of Maple Grove who are connected to th

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 $82, while one using 1600 cubic feet was billed $123. What is the charge in dollars per cubic foot? Give an exact answer: 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. C(w) = How many cubic feet of water used would lead to a bill of $140? Round your answer to the nearest cubic foot. ft^3

Solution

b. C(w) = y + w*x

let y be fixed cost

x be cost per cubic foot

Acc to question

82 = y + 1000x..1

123 = y + 1600x........2

2 - 1

600x = 41

x = 41/600

putting value of x in eq 1

82- 1000*41/600 = y

82 - 410/6 = y

492 - 410 / 6 = y

y = 82/6 = 41/3

C(w) = 41/3 + 41/600w

C(w) = (8200+41w)/600

c) C(w) = 140$

C(w) = (8200+ 41w)/600

140 *600 = 8200 + 41w

(84000-8200) /41 = w

75800/41= w

w = 1848.78 cubic feet