how would you write this as an algebraic equation?

Question

i can see it, but i am having trouble getting it on paper!
Water bill is equal to $55 for the first 6000 gals. (or any protion thereof) plus the number of gallons used in excess of 6000 gallons times $0.20 per gallon.

Answer 1

Let x be the amount of gallons you used:

There is a flat charge of $55 for the first 6,000 gallons. So start with that.

Then you need to add the excess charge. The charge is 0.20 per gallon over 6000.

The hard part is figuring out how to write the excess of 6000 gallons. If I had used 7000, it would be 1000. If I had used 8000, it would be 2000. So in general, you would write (x - 6000).

Putting it all together:
Water bill = 55 + (x - 6000) * 0.20

Now technically, you have two formulas. You have one for amounts under 6000, and one for amounts over 6000.

For x <= 6000,
f(x) = 55

For x > 6000
f(x) = 55 + (x - 6000) * 0.20

Answer 2

W = 55 + 0.20(g - 6000), where g is the number of gallons used AND g > 6000. The g - 6000 is the number of gallons used in excess of 6000.

To set it up as a generally useful Excel formula, you'd have to use an IF function to compute it one way for g<6000 and the other for g>6000. It's the sort of thing you might have to do on quite a lot of office jobs.

Answer 3

you have 55+.2x with x being the number of gallons over 6000 that were used.

Answer 4

55 + .2(x-6000) = total