PLEASE TYPE OUT THE ANSWER SO I CAN BETTER UNDERSTAND IT, NO PICTURES PLEASE. TH

Question

PLEASE TYPE OUT THE ANSWER SO I CAN BETTER UNDERSTAND IT, NO PICTURES PLEASE. THANKS!

A gas company has the following rate schedule for natural gas usage in single-family residences: Monthly service charge $8.80 Per therm service charge 1st 25 therms Over 25 therms $0.6686/therm $0.85870/therm What is the charge for using 25 therms in one month? Show your work. What is the charge for using 45 therms in one month? Show your work. Construct a function that gives the monthly charge C for x therms of gas.

Explanation / Answer

25 therms :
For 1st 25 therms, we would spend 0.6686 per therm.
So, for exactly 25 therms, total spending is 25 * 0.6686, i.e 16.715
dollars.

And add the service charge,
total charge bcomes :

C = 8.80 + 16.715

25.515 dollars

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45 therms :
Upto 25 therms, we spend 25.515 dollars

For the next 20 therms, we spend 0.85870 per therm
So, 25.515 + 20*0.85870

42.689 dollars ---> ANS

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Upto 25 therms, we have the formula :
8.80 + 0.6686x

After 25 therms, the remaining x-25 therms go at 0.85870 per therm

So, 8.80 + 0.6686*25 + 0.85870(x - 25) ; x > 25

25.515 + 0.85870x - 21.4675

0.85870x + 4.0475 ; x > 25

So, the function is :
C = 0.6686x + 8.80 ; x <= 25
C = 0.85870x + 4.0475 ; x > 25

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