A residential water bill is based on a flat fee of $10 plus a charge of 0.75 for each 1000 gal of water used find the number of gallons of water a family can use and have a monthly water bill that is less than 37$

To determine the maximum number of gallons of water a family can use while keeping their monthly water bill under $37, we can set up the problem as follows:

1. The total water bill $ B $ is given by the formula:

\[
B = 10 + 0.75 \times \text{(number of 1000 gallons used)}
\]

2. We want to find the maximum number of 1000-gallon units the family can use so that the bill is less than $37.

\[
10 + 0.75x < 37
\]

Where $ x $ represents the number of 1000-gallon units used.

Now, solve for $ x $:

1. Subtract 10 from both sides:

\[
0.75x < 27
\]

2. Divide both sides by 0.75:

\[
x < \frac{27}{0.75}
\]

3. Simplify the division:

\[
x < 36
\]

So, $ x $ (the number of 1000-gallon units) must be less than 36.

Therefore, the family can use **up to 35,999 gallons** of water in a month to keep their bill under $37, since $ x = 35.999 $ (which is slightly less than 36 units, or 36,000 gallons).

Would you like more details, or do you have any questions?

Here are 5 related questions to explore further:

1. What would the water bill be if the family used exactly 36,000 gallons?
2. How would the maximum number of gallons change if the flat fee were increased to $15?
3. If the water rate increased to $1 per 1000 gallons, how many gallons could the family use while staying under $37?
4. What would be the impact on the water bill if the family reduced their usage by 10% each month?
5. How would the water bill be affected if there were an additional surcharge per gallon for exceeding a certain usage limit?

**Tip:** When dealing with cost-related problems, always isolate the variable representing the quantity (like the number of gallons) to easily determine the allowable usage within a budget.

Learn how to calculate the maximum gallons of water a family can use to keep their monthly bill under $37. This problem involves solving a linear inequality based on a flat fee and a per-gallon charge. Discover the solution step-by-step with detailed arithmetic operations. Suitable for students in Grades 6-8.

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