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 ranges from $54 to $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.)

a 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be from 17.7 to 37.6 HCF.
b 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be from 17.7 to 58.2 HCF.
c 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be from 38.2 to 78.7 HCF.
d 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be from 58.9 to 78.7 HCF.

1 answer

The correct compound inequality to represent the scenario is:
54 ≤ 1.41x + 29 ≤ 82

To determine the recommended range of water consumption, we first need to solve for x:
Subtract 29 from all parts of the inequality:
25 ≤ 1.41x ≤ 53
Divide all parts by 1.41:
17.7 ≤ x ≤ 37.6

Therefore, the recommended range of water consumption is from 17.7 to 37.6 HCF, which corresponds to option a.