Let $x$ represent the amount of water (in gallons) that each family member can use for the remainder of the month.

The Green family can use up to 9,750.05 gallons per month, and they have already used 4,885.78 gallons. Therefore, the amount of water they have left is:

$9,750.05 - 4,885.78 = 4,864.27 \text{ gallons}$

Since there are 6 members in the family, each member's remaining water usage must satisfy the inequality:

$6x \leq 4,864.27$

To find the maximum amount of water one family member can use, divide both sides of the inequality by 6:

$x \leq \frac{4,864.27}{6} \approx 810.71$

Thus, each family member can use at most 810.71 gallons of water for the remainder of the month. The inequality is:

$x \leq 810.71$

This shows that each member can use up to 810.71 gallons of water.

Would you like to go into more detail or have any questions?

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Here are 5 related questions for further exploration:

1. What if the Green family had already used 5,500 gallons? How much could each member use then?
2. If one family member used 850 gallons last month, how would that affect the remaining water distribution for the others?
3. How much water per month would the Green family have if their water limit increased to 12,000 gallons?
4. If the drought limit decreased to 8,000 gallons, how much would each family member be allowed to use for the rest of the month?
5. How much water has each member used so far this month, based on the current usage?

Tip: Always double-check your units when calculating problems involving rates or limits to avoid small errors!