Let's break down the problem step by step to arrive at the solution.
1. Understanding the Given Data:
- The Montanez family consists of 4 members.
- They have used 3,485.78 gallons of water so far this month.
- They cannot exceed a monthly limit of 7,250.50 gallons.
2. Calculating the Remaining Water Allowance:
- To find out how much water remains for the rest of the month, subtract the amount of water already used from the total allowance:
[tex]\[
\text{Remaining Allowance} = 7,250.50\ \text{gallons} - 3,485.78\ \text{gallons} = 3,764.72\ \text{gallons}
\][/tex]
3. Distributing the Remaining Allowance Among Family Members:
- The remaining water needs to be equally divided among the 4 family members. Therefore:
[tex]\[
\text{Per Member Allowance} = \frac{3,764.72\ \text{gallons}}{4} = 941.18\ \text{gallons}
\][/tex]
4. Formulating the Inequality:
- We need to write an inequality that shows how much water one member of the family can use for the remainder of the month.
- Let [tex]\( x \)[/tex] represent the amount of water each member can still use.
- The total water used by the 4 members for the rest of the month plus the water already used should not exceed the total monthly allowance. Thus, the inequality should be:
[tex]\[
4x + 3,485.78 \leq 7,250.50
\][/tex]
Given that [tex]\(x\)[/tex] represents the amount of water each person can use for the remainder of the month:
- The correct inequality is:
[tex]\[
4x + 3,485.78 \leq 7,250.50
\][/tex]
Therefore, the correct answer among the options provided is:
[tex]\[
4x + 3,485.78 \leq 7,250.50
\][/tex]
