Final answer:
To find the range of water consumption for customers with a monthly charge between $35 and $50, use the equation C = 10.40 + 0.0059G and set up two inequalities. Solve the inequalities to get a minimum consumption of approximately 4169 gallons and a maximum consumption of approximately 6712 gallons.
Step-by-step explanation:
The question involves finding the range of water consumption in gallons for customers whose monthly charge is between $35 and $50, given the county water department's pricing structure. The water department charges a monthly administration fee of $10.40 plus $0.0059 per gallon of water used.
Let G be the number of gallons of water used. The total cost, C, is given by the equation C = 10.40 + 0.0059G. To find the minimum and maximum water consumption for the given range of monthly charges, we will set up two inequalities:
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- 35 ≤ 10.40 + 0.0059G (Minimum consumption for a charge of at least $35)
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- 50 ≥ 10.40 + 0.0059G (Maximum consumption for a charge no more than $50)
To solve the first inequality:
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- 35 - 10.40 ≤ 0.0059G
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- 24.60 ≤ 0.0059G
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- G ≥ 4169.49 gallons
To solve the second inequality:
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- 50 - 10.40 ≥ 0.0059G
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- 39.60 ≥ 0.0059G
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- G ≤ 6711.86 gallons
Therefore, the minimum water consumption is approximately 4169 gallons, and the maximum is approximately 6712 gallons to ensure that the monthly charge is at least $35 but no more than $50.