Question

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)

60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 69.1 and 87.5 HCF.
60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 44.1 and 87.5 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 37.5 and 44.1 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

Answer 1

(d) 60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF

Explanation:

You want an inequality and its solution for the recommended range of water consumption, given water is billed at $34 plus $1.36 per hundred cubic feet (HCF), and the recommended bill is between $60 and $85.

Bill amount

For x hundred cubic feet of consumption, the charge will be 1.36x. When that is added to the $34 monthly fee, the monthly bill is 1.36x +34.

Since it is recommended this amount be between $60 and $85, we can write the inequality as ...

60 ≤ 1.36x +34 ≤ 85

Consumption

Solving this inequality for x, we have ...

26 ≤ 1.36x ≤ 51 . . . . . . . subtract 34

19.1 ≤ x ≤ 37.5 . . . . . . . divide by 1.36, round to 1 dp

To stay within the recommended range of water consumption, the usage should be between 19.1 and 37.5 HCF.

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