Question

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 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.) 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 37.6 HCF. 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 58.2 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 38.2 and 78.7 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 58.9 and 78.7 HCF.

Answer 1

To represent the scenario in a compound inequality, use the formula: 54 ≤ 1.41x + 29 ≤ 82. The recommended range of water consumption is between 17.7 and 37.6 HCF.

Step-by-step explanation:

To represent the scenario in a compound inequality, we use the formula:

54 ≤ 1.41x + 29 ≤ 82

To determine the recommended range of water consumption, we need to isolate x.

Subtracting 29 from all the parts of the compound inequality, we get:

25 ≤ 1.41x ≤ 53

Then, dividing all parts of the compound inequality by 1.41, we get:

17.7 ≤ x ≤ 37.6

Therefore, the recommended range of water consumption is between 17.7 and 37.6 HCF.