Residents Of The Town Of Maple Grove Who Are...

Anonymous

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Residents of the town of Maple Grove who are connected to 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 $90, while one using 1600 cubic feet was billed $105. What is the charge per cubic foot? How do you wite an equation for the total cost of a residen'ts water as a function of cubic feet of water used? How many cubic feet of water used would lead to a bill of $130. I am lost from the beginning of how to start this problem.

 

Answer No.1

Anonymous

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You must make a system of equations. Let x equal the charge per cubic foot. Let y equal the yearly fixed amount. 1000x + y = 90 1600x + y = 105 You can use elimination to get rid of the y's. 1000x + y = 90 -1600x - y = -105 ______________ -600x = -15 x = $0.025 1000(0.025) + y = 90 y = 90 - 25 y = $65 The charge per cubic foot is $0.025. The equation for the total cost C is C(x) = 0.025x + 65 130 = 0.025x + 65 0.025x = 65 x = 2600 cubic feet NOTE: THE RESPONSE ABOVE MADE AN ERROR IN SUBTRACTION. 130 - 65 = 65 (not 75)

Answer No.2

JonnyTeacher9

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Let the fixed cost be b: Then customer 1: b+m*1000 = 90 2: b+m*1600 = 105 That's 2 eqns in 2 variables: 600m= 15 m = 15/600 = 0.025 Get b from either eqn: b+1000*0.025 = 90 b = 90-25 = 65 So, cost = 65 + 0.025*x , where x is the number of cu ft used. So, for a cost of 130 130 = 65 + 0.025*x x = (130-65)/0.025 = 75/0.025 = 3000 cu ft

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