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.)

Answer 1

The inequality: 54 ≤ 29 + 1.41x ≤ 82

The recommended range of water consumption is between 17.7 HCF and 37.6 HCF

Given: Water utility charges fee = $29

Additional fee per hundred cubic (HCF) feet of water = $1.41

x : representing monthly water usage

The recommended monthly bill for household is between $54 and $82

Let us calculate the monthly usage bill in terms of x.

Monthly bill = Water utility charges fee + Additional fee per hundred cubic (HCF) feet of water * x

Monthly bill = 29 + 1.41x

According to the question Monthly bill is recommended to lie in range

54 ≤ Monthly bill ≤ 82

=> 54 ≤ 29 + 1.41x ≤ 82

The compound inequality representing the scenario given in the question is : 54 ≤ 29 + 1.41x ≤ 82

Now we need to find the recommended range for x.

Therefore,

54 ≤ 29 + 1.41x ≤ 82

54 - 29 ≤ 29 + 1.41x - 29 ≤ 82 - 29

25 ≤ 1.41x ≤ 53

25 / 1.41 ≤ 1.41x / 1.41 ≤ 53 / 1.41

17.7 ≤ x ≤ 37.6

Hence the recommended range of water consumption is between 17.7 HCF and 37.6 HCF

Know more about "compound inequality" here: https://brainly.com/question/20296065

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