The equation
P
=
31
+
3.81
w
models the relation between the monthly water bill payment,
P
, in dollars, and the amount of water used in a month by Arturo,
w
, in thousands of gallons.

a)  Find the payment when Arturo uses 0 gallons of water in a month.

Select an answer
.

b)  Find the payment when Arturo uses 12 thousand gallons of water in a month.

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.

The equation P = 31 + 3.81w models the relation between the monthly water bill payment, P, in dollars, and the amount of water used in a month by Arturo, w, in thousands of gallons.

(a) Find the payment when Arturo uses 0 gallons of water in a month.

(b) Find the payment when Arturo uses 12 thousand gallons of water in a month.

Learn how to calculate Arturo's monthly water bill payment using the linear equation P = 31 + 3.81w. This problem covers basic algebraic concepts, focusing on calculating payments for different water usage levels. Suitable for students in Grades 6-8.

Math Problem Statement

The equation P

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation