Question

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additional$1.28 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $57 and$87 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) 057 ≤1.28x-38 s 87; To stay within the range, the usage should be between 44.5 and 97.7 HCF.

B) 57 s 1.28x – 38 s 87; To stay within the range, the usage should be between 74.2 and 97.7 HCF.

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

D)57 s 1.28x+38 ≤ 87; To stay within the range, the usage should be between 14.8 and 67.9 HCF.

1. Latifah
Using a linear function, the correct option regarding the situation is given by:
C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

### What is a linear function?

A linear function is modeled by:
y = mx + b
In which:
• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The bill is modeled by a linear function, with an intercept of $38 and a slope of$1.28, hence it is given by:
C(x) = 1.28x + 38
The bill should be between $57 and$87 dollars per month, hence:
57 <= C(x) <= 87.
The values of x are:
C(x) >= 57
1.28x + 38 >= 57
x >= 19/1.28
x >= 14.8.
C(x) >= 87
1.28x + 38 >= 87
x >= 49/1.28
x >= 38.3.
Hence option C is correct.
More can be learned about linear functions at https://brainly.com/question/24808124
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