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.
a) for 25 therms
cost = $.6686(25)) = $16.72
b) cost = 16.72 + (45-25)(.8587
= $33.89
c) cost = (x-25)(.8587) + 16.72 , for x > 25
or = .6686x , for 0 < x ≤ 25
To find the charges for using a specific number of therms in a month, we need to account for the monthly service charge as well as the per therm service charges.
(a) To calculate the charge for 25 therms, we only need to consider the per therm service charge for the first 25 therms. The charge for 25 therms is given by:
Charge for 25 therms = (Number of therms * per therm service charge) + monthly service charge
In this case:
Number of therms = 25
Per therm service charge = $0.6686
Charge for 25 therms = (25 * $0.6686) + $8.80
Charge for 25 therms = $16.715 + $8.80
Charge for 25 therms = $25.515
Therefore, the charge for using 25 therms in one month is $25.515.
(b) To calculate the charge for 45 therms, we need to consider both the per therm service charge for the first 25 therms and the additional per therm service charge for the remaining therms. The charge for 45 therms is given by:
Charge for 45 therms = (Number of therms * per therm service charge) + monthly service charge
In this case:
Number of therms = 45
Per therm service charge for the first 25 therms = $0.6686
Per therm service charge for the remaining therms = $0.85870
Charge for 45 therms = (25 * $0.6686) + ((45 - 25) * $0.85870) + $8.80
Charge for 45 therms = $16.715 + ($0.85870 * 20) + $8.80
Charge for 45 therms = $16.715 + $17.174 + $8.80
Charge for 45 therms = $42.689
Therefore, the charge for using 45 therms in one month is $42.689.
(c) To construct a fraction that gives the monthly charge c for x therms of gas, we can use the formula:
c = (Number of therms * per therm service charge) + monthly service charge
In this case:
Number of therms = x
Per therm service charge for the first 25 therms = $0.6686
Per therm service charge for the remaining therms (over 25 therms) = $0.85870
So, the fraction that gives the monthly charge c is:
c = (x * $0.6686) + ((x - 25) * $0.85870) + $8.80
c = ($0.6686x) + ($0.85870(x - 25)) + $8.80
This fraction represents the monthly charge c for x therms of gas.