The equation P

The equation $P = 31 + 3.81w$ represents the monthly water bill payment $P$ in dollars, where $w$ is the amount of water used in a month in thousands of gallons.

Part (a): Payment when Arturo uses 0 gallons of water

To find the payment when $w = 0$:

$P = 31 + 3.81(0) = 31$

So, the payment is $31.

Part (b): Payment when Arturo uses 12 thousand gallons of water

To find the payment when $w = 12$:

$P = 31 + 3.81(12) = 31 + 45.72 = 76.72$

So, the payment is $76.72.

Let me know if you'd like further details or have any questions.

Here are some related questions:

1. What does the constant value 31 represent in the equation?
2. How does the value 3.81 affect the payment as the water usage increases?
3. What would the payment be if Arturo used 6 thousand gallons of water?
4. How could you modify the equation if a different base rate was applied, say $25 instead of $31?
5. What is the percentage increase in payment when Arturo uses 12 thousand gallons instead of 0 gallons?

Tip: To understand real-life application problems like this, focus on what each number in the equation represents—this helps in interpreting results effectively.