Sure, let's solve the problem step-by-step.
### Step 1: Calculate Remaining Water Limit
First, we need to determine how much water the Lamaster family can still use for the rest of the month. They have already used \(4,885.78\) gallons, and their monthly limit is \(7,250.50\) gallons. The remaining water limit can be calculated by subtracting the amount of water already used from the monthly limit:
[tex]\[
7,250.50 - 4,885.78 = 2,364.72
\][/tex]
So, the family has \(2,364.72\) gallons of water left to use for the remainder of the month.
### Step 2: Calculate Water Allocation Per Family Member
We assume that each family member will use the same amount of water for the rest of the month.
Since there are 5 family members, we divide the remaining water limit by the number of family members:
[tex]\[
\frac{2,364.72}{5} = 472.944
\][/tex]
This means each family member can use up to \(472.944\) gallons of water for the remaining part of the month.
### Step 3: Inequality to Represent Water Use Boundaries
To formulate an inequality that represents the boundaries of water use for one family member, we need to set up an equation that includes the total monthly water limit:
Let \( x \) be the amount of water one family member can use. Since there are 5 family members, the total water used by the family would be \(5x\) for the remainder of the month. Adding this to the water already used (\(4,885.78\) gallons) must be less than or equal to the monthly limit (\(7,250.50\)) gallons.
Thus, the inequality is:
[tex]\[
5x + 4,885.78 \leq 7,250.50
\][/tex]
This inequality ensures that the total water usage of the family for the month does not exceed the allowed limit.
So, among the given options, the correct inequality is:
[tex]\[
5x + 4,885.78 \leq 7,250.50
\][/tex]
