Answer to Question #168467 in Algebra for Elle

Question

Solve the problem.

A gas company has the following rate schedule for natural gas usage in single-family residences:

The monthly service charge$8.80

 

Per therm service charge1st 25 therms$0.6686/them over 25 therms$0.85870/therm

What is the charge for using 25 therms in one month?

What is the charge for using 45 therms in one month?

Construct a function that gives the monthly charge C for x therms of gas.

Answer 1

Monthly service charge = $8.80

Per therm service charge for 1st 25 therms = $0.6686/therm

Per therm service charge after 1st 25 therms = $0.85870/therm

Charge for using 25 therms in one month = monthly service charge + (0.6686 × 25)

= 8.80 + 16.715

= $25.515

Charge for using 45 therms in one month = monthly service charge + (0.6686 × 25) + (0.85870 × 20)

= 8.80 + 16.715 + 17.174

= $42.689

Function to give the monthly charge C for x therms of gas is given as follows:

C = monthly service charge + (x × 0.6686) for 0$\lt$ x $\le$ 25

$\therefore$ C = $ 8.80 + (x × 0.6686) for 0$\lt$ x $\le$ 25

C = monthly service charge + (25 × 0.6686) + ((x - 25) × 0.85870) for x $\gt$ 25

C = 8.80 + 16.715 + (x × 0.85870) - (25 × 0.85870) for x $\gt$ 25

C = 25.515 - 21.4675 + (x × 0.85870) for x $\gt$ 25

$\therefore$ C = $ 4.0475 + (x × 0.85870) for x $\gt$ 25