A utility company has the following rate schedule for natural gas usage in a city's district: Monthly service charge of $8.80; Per therm service charge: 1st 25 therms: $0.6686/therm; Over 25 therms: $0.85870
(a) What is the charge for usaging 25 therms in one month?
(b) What is the charge for using 45 therms in one month?
(c) Construct a fraction that gives the monthly charge c for x therms of gas.
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To calculate the charges for natural gas usage, we need to consider the monthly service charge and the per therm charges based on the usage. Let's solve each part of the question step by step:
(a) Charge for using 25 therms in one month:
- Monthly service charge: $8.80
- Per-therm service charge: $0.6686/therm for the first 25 therms
To calculate the charge, multiply the per therm service charge by the number of therms used:
Charge = Per Therm Service Charge * Number of Therms
Charge = $0.6686/therm * 25 therms
Therefore, the charge for using 25 therms in one month is:
Charge = $0.6686/therm * 25 therms = $16.72
(b) Charge for using 45 therms in one month:
- Monthly service charge: $8.80
- Per-therm service charge: $0.6686/therm for the first 25 therms, $0.85870/therm for the remaining therms
To calculate the charge, we need to consider the charge for the first 25 therms separately and the charge for the remaining therms separately:
Charge = Per Therm Service Charge * Number of Therms
Charge = $0.6686/therm * 25 therms + $0.85870/therm * (45 - 25) therms
Therefore, the charge for using 45 therms in one month is:
Charge = $0.6686/therm * 25 therms + $0.85870/therm * (45 - 25) therms
Charge = $16.72 + $17.15 = $33.87
(c) To construct a fraction that gives the monthly charge (c) for x therms of gas:
- Monthly service charge: $8.80
- Per-therm service charge: $0.6686/therm for the first 25 therms, $0.85870/therm for the remaining therms
The fraction would be:
c = ($8.80 + Per Therm Service Charge * (x - 25)) / x
Make sure to substitute the correct Per Therm Service Charge for the first 25 therms and the remaining therms when using the formula.
Note: It is important to refer to the utility company's official rate schedule for the most accurate and up-to-date information on charges.