Math Problem Statement

The information below is taken from a water bill for the month of July. Previous Reading: 23,757 kL New Reading: 24,647 kL Water Rate: $2.50 per kL Meter Rental: $25 per month Calculate: (a) the variable cost of the bill. (b) the fixed cost of the bill. (c) the total cost of the water bill.

Solution

Let's analyze the image for the water bill calculation.

Given Data:

  • Previous Reading: 23,757 kL
  • New Reading: 24,647 kL
  • Water Rate: $2.50 per kL
  • Meter Rental: $25 per month

We are asked to calculate:

  1. The variable cost of the bill.
  2. The fixed cost of the bill.
  3. The total cost of the water bill.

Solution:

(a) Variable Cost of the Bill:

The variable cost depends on the amount of water used, which is: Water Usage=New ReadingPrevious Reading=24,647kL23,757kL=890kL\text{Water Usage} = \text{New Reading} - \text{Previous Reading} = 24,647 \, \text{kL} - 23,757 \, \text{kL} = 890 \, \text{kL} Now, multiply the water usage by the rate per kL: Variable Cost=890kL×2.50$/kL=2,225$\text{Variable Cost} = 890 \, \text{kL} \times 2.50 \, \text{\$/kL} = 2,225 \, \text{\$}

(b) Fixed Cost of the Bill:

The fixed cost is the monthly meter rental, which is given as: Fixed Cost=25$\text{Fixed Cost} = 25 \, \text{\$}

(c) Total Cost of the Water Bill:

The total cost is the sum of the variable and fixed costs: Total Cost=Variable Cost+Fixed Cost=2,225$+25$=2,250$\text{Total Cost} = \text{Variable Cost} + \text{Fixed Cost} = 2,225 \, \text{\$} + 25 \, \text{\$} = 2,250 \, \text{\$}

Final Answers:

  • (a) Variable Cost: $2,225
  • (b) Fixed Cost: $25
  • (c) Total Cost: $2,250

Would you like further clarification on any part of this? Here are some related questions:

  1. How would the cost change if the water rate increased to $3.00 per kL?
  2. What would happen if the meter rental was billed quarterly instead of monthly?
  3. How does the variable cost impact the total bill as water usage increases?
  4. Could the fixed cost ever be more than the variable cost? Under what conditions?
  5. What would the total cost be if no water was used during the billing period?

Tip: To better manage water bills, tracking consumption trends can help predict future costs.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic
Rates
Fixed Costs

Formulas

Variable Cost = (New Reading - Previous Reading) * Water Rate
Fixed Cost = Meter Rental
Total Cost = Variable Cost + Fixed Cost

Theorems

-

Suitable Grade Level

Grades 6-8