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.
well, for x <= 25,
f(x) = 8.80 + 0.6686x
Now what about for x > 25?
To calculate the charges for the given rate schedule, we need to follow the specified rates and apply them to the given gas usage.
(a) To calculate the charge for using 25 therms in one month:
- First, we need to determine the per therm charge for the first 25 therms, which is $0.6686/therm.
- Multiply the per therm charge by the number of therms used:
25 therms * $0.6686/therm = $16.715
To summarize, the charge for using 25 therms in one month is $16.715.
(b) To calculate the charge for using 45 therms in one month:
- We have two different rate categories here: the first 25 therms and the additional therms over 25.
- Calculate the charge for the first 25 therms as we did in part (a):
25 therms * $0.6686/therm = $16.715
- For the remaining therms (45 - 25 = 20 therms), we need to calculate the charge using the rate for over 25 therms:
20 therms * $0.85870/therm = $17.174
- Add these charges together:
$16.715 + $17.174 = $33.889
To summarize, the charge for using 45 therms in one month is $33.889.
(c) To construct a fraction that gives the monthly charge c for x therms of gas:
- Let's break down the monthly charge into its components:
- Monthly service charge: $8.80
- For the first 25 therms: $0.6686/therm
- For the additional therms over 25: $0.85870/therm
- Using this information, we can construct the fraction:
c = ($8.80 + $0.6686 * x) + ($0.85870 * (x - 25))
c = $8.80 + $0.6686x - $0.85870 * 25 + $0.85870x
Simplifying further:
c = $8.80 + $0.6686x - $21.4675 + $0.85870x
c = $8.80 - $21.4675 + ($0.6686 + $0.85870)x
c = ($8.80 - $21.4675) + ($0.6686 + $0.85870)x
c = ($8.80 - $21.4675) + $1.5273x
Hence, the fraction that gives the monthly charge c for x therms of gas is:
c = ($8.80 - $21.4675) + $1.5273x