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 $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

Explanation / Answer

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

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