Question

Can I get some help solving this massive problem please? Thanks!

Answer 1

See below:

Explanation:

The gas company, regardless of how much gas you use in a single month, charges a monthly service charge of $8.80. No matter what, we have to pay that.

The gas company then has a 2-tier system of charging for gas - if you use 25 therms or less, you get charged $0.6686/therm. If you use more than the 25, you get charged a higher rate for every therm above the initial 25, $0.8587/therm.

25 therms

So in a month where we use 25 therms, we pay the monthly charge of $8.80, plus the therm charge, which is:

`25xx.6686=$16.715`

And so for the month we pay:

`$color(white)(0)8.80` - monthly charge
`ul($16.715` - per therm charge
`$25.515` - total charge for the month, which rounds to `$25.52`

45 therms

We know how much it costs for 25 therms - we've included the monthly charge and the therm charge (I'll use the unrounded figure here - no sense in giving the gas company an extra half cent!). And so what we need to know is the charge for the extra 20 therms. That's:

`20xx.8587=$17.174`

This gives us:

`$color(white)(0)8.80` - monthly charge
`$16.715` - per therm charge, first 25
`ul($17.174)` - per therm charge, 20 at the higher rate
`$42.689` - total charge for the month, rounded to `$42.69`

Function

This is a step function where `C` is the cost and `x` is the gas used per month. We can write it this way:

`x=|_(x>25, C=$25.515+$0.8587x)^(x<=25, C=$8.80+$0.6686x)`