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.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Water utility charges = $34

Additional per hundred cubic feet (HCF) of water = $1.36

x represents the water usage in HCF in a household

The recommended monthly bill for a household is between $60 and $85

So, the monthly bill in terms of x is given as,

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

⇒Monthly bill = 34 + 1.36x

Since monthly bill or a household is between $60 and $85

Therefore we can write,

60 ≤ monthly bill ≤ 85

or,

60 ≤ 34 + 1.36x ≤ 85

Hence,a compound inequality to represent the scenario is

60 ≤ 34 + 1.36x ≤ 85

Now for recommended range of x solving the above inequality,

60 ≤ 34 + 1.36x ≤ 85

or, 60 -34 ≤ 34 + 1.36x -34 ≤ 85 -34

or, 26 ≤ 1.36x ≤ 51

or, 26/1.36 ≤ 1.36x/1.36 ≤ 51/1.36

or, 19.11 ≤ x ≤ 37.5

Hence, the recommended range of water consumption is between 19.11 HCF and 37.5 HCF

To learn more about compound inequality: https://brainly.com/question/9958682

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