Math Problem Statement

Adjust the pie chart to represent the source of customer contacts based on the given information about customer communication methods.

Solution

From the information shown in the image:

Key Information:

  1. 500 customers contacted the company today.
  2. Contact breakdown:
    • Phone: 250 customers.
    • Email: 50% of the Phone contacts = 250×0.5=125250 \times 0.5 = 125.
    • Social Media: Denoted as a base value.
    • Webchat: 4 times the Social Media contacts.

Let us calculate the number of Social Media and Webchat contacts.

Step 1: Total Contacts Equation

The total contacts equation is: Phone+Email+Social Media+Webchat=500\text{Phone} + \text{Email} + \text{Social Media} + \text{Webchat} = 500

Substitute known values: 250+125+x+4x=500250 + 125 + x + 4x = 500

Step 2: Simplify

375+5x=500375 + 5x = 500

Step 3: Solve for xx (Social Media contacts)

5x=125x=255x = 125 \quad \Rightarrow \quad x = 25

Step 4: Calculate Webchat contacts

Webchat=4×Social Media=4×25=100\text{Webchat} = 4 \times \text{Social Media} = 4 \times 25 = 100

Final Breakdown:

  • Phone: 250 contacts.
  • Email: 125 contacts.
  • Social Media: 25 contacts.
  • Webchat: 100 contacts.

Pie Chart Percentages:

  • Phone: 250500×100=50%\frac{250}{500} \times 100 = 50\%.
  • Email: 125500×100=25%\frac{125}{500} \times 100 = 25\%.
  • Social Media: 25500×100=5%\frac{25}{500} \times 100 = 5\%.
  • Webchat: 100500×100=20%\frac{100}{500} \times 100 = 20\%.

Adjust the Pie Chart:

The pie chart should reflect the following percentages:

  • Phone: 50%.
  • Email: 25%.
  • Social Media: 5%.
  • Webchat: 20%.

Let me know if you want additional details or explanations!


5 Related Questions:

  1. What is the formula for calculating percentages in a pie chart?
  2. How can we double-check calculations for proportional values in such problems?
  3. What tools can be used to create accurate pie charts?
  4. How does the allocation of percentages relate to total values?
  5. Could this type of data representation be misleading? Why or why not?

Tip:

Always ensure the total percentage in a pie chart equals 100% by verifying calculations for each segment.

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Math Problem Analysis

Mathematical Concepts

Percentages
Proportional Reasoning
Equation Solving

Formulas

Percentage = (Part / Total) × 100
Total Contacts = Phone + Email + Social Media + Webchat

Theorems

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Suitable Grade Level

Grades 5-8