A municipal water department charges each household a fixed monthly service fee plus a constant rate per hundred cubic…

To determine Household X's total bill in July, model the billing structure with a linear equation. Let S represent the fixed monthly service fee in dollars, and let r represent the rate in dollars per HCF of water consumed.

For June, the bills for Household X and Household Y can be written as:

(1) S + r · w = A

(2) S + r · (1.5w) = B

Subtracting equation (1) from equation (2) eliminates S:

1.5rw - rw = B - A

0.5rw = B - A

rw = 2(B - A)

In July, Household X reduced its water consumption by 20% compared to June, so it consumed w - 0.20w = 0.80w HCF of water. Household X's July bill is:

Bill = S + r · (0.80w) = (S + rw) - 0.20rw

Since S + rw = A and rw = 2(B - A), substitute these into the expression:

Bill = A - 0.20[2(B - A)]

Bill = A - 0.40(B - A)

Bill = A - 0.40B + 0.40A

Bill = 1.4A - 0.4B

Choice A is incorrect because it adds the 20% consumption change to June's bill instead of subtracting it (A + 0.4(B - A) = 0.6A + 0.4B), incorrectly representing an increase in the bill.

Choice B is incorrect because it results from multiplying by 0.5 instead of dividing by 0.5 when solving 0.5rw = B - A, giving rw = 0.5(B - A) and a July bill of A - 0.20(0.5(B - A)) = 1.1A - 0.1B.

Choice C is incorrect because it fails to divide the difference in bills by 0.5, assuming that the difference in consumption was w rather than 0.5w, which yields rw = B - A and a July bill of A - 0.20(B - A) = 1.2A - 0.2B.