Problem 321 - Elementary Algebra

Question

In the following exercises, solve. Jake's water bill is \(\$ 24.80\) per month plus \(\$ 2.20\) per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than \(\$ 60\) ?

Step-by-Step Solution

Answer

Jake can use a maximum of 16 ccf of water.

Step 1: Identify the variables

Let’s define the variable. Let’s use c to represent the number of ccf (hundred cubic feet) of water Jake can use.

Step 2: Set up the equation

Jake’s water bill consists of a fixed part of \$ 24.80 per month and an additional cost of \$ 2.20 per ccf. Therefore, the total cost of the bill can be expressed as: \ \( 24.80 + 2.20c \).

Step 3: Formulate the inequality

Jake wants his bill to be no more than \$ 60. Set up the inequality: \ \( 24.80 + 2.20c \leq 60 \)

Step 4: Isolate the variable

Subtract \$ 24.80 from both sides of the inequality to isolate the term with c: \ \( 2.20c \leq 60 - 24.80 \)

Step 5: Simplify the inequality

Perform the subtraction on the right side: \ \( 2.20c \leq 35.20 \)

Step 6: Solve for the variable

Divide both sides by \ \(2.20\) to solve for c: \ \( c \leq \frac{35.20}{2.20} \)

Step 7: Calculate the maximum number of ccf

Perform the division to find c: \ \( c \leq 16 \)

Key Concepts

setting up linear equations

To solve problems like Jake's water bill, you first need to set up a linear equation. This means forming an equation that represents the problem situation. For Jake's water usage, we identified the fixed monthly cost of \(24.80 and the variable cost of \)2.20 per ccf. Setting up the equation involves combining these into a single expression: \(24.80 + 2.20c\). Here, \