Mean Algebra Word Problem Game

Mean Algebra Word Problem Quiz/Game
This game focuses on solving word problems involving Arithmetic Mean logic. Scroll down the page for a more detailed explanation.

 

 

How to Play the Mean Algebra Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Mean Algebra Word Problems
The “Mean” (or Average) is defined by the formula:

\(\text{Mean} = \frac{\text{Total Sum of all values}}{\text{Number of values (n)}}\)

Most algebra word problems are easier to solve if you rearrange this to find the Total Sum first:

\(\text{Total Sum} = \text{Mean} \times n\)

Strategy 1: The Missing Value (The “New Member”)
Problem: The mean of 4 numbers is 15. If three numbers are 10, 12, and 18, what is the fourth?
Find the Goal Total: 4 numbers} × 15 = 60
Find the Current Total: 10 + 12 + 18 = 40
Subtract to find the missing value: 60 - 40 = 20
Check: (10 + 12 + 18 + 20) divide; 4 = 15.

Strategy 2: Changing the Mean
Problem: A student averages 80% on 3 tests. What must they score on the 4th test to raise their average to 85%?
Old Total: 3 tests} × 80 = 240
New Goal Total: 4 tests × 85 = 340
The Difference: 340 - 240 = 100
The student needs a 100% on the next test.

Strategy 3: Weighted Averages
Problem: 10 students scored 70 and 20 students scored 100. What is the mean for the whole class?
You cannot simply average 70 and 100 (85) because there are more students in the second group.
Group A Total: 10 × 70 = 700
Group B Total: 20 × 100 = 2,000
Grand Total: 700 + 2,000 = 2,700
Total Students (n): 10 + 20 = 30
Weighted Mean: 2,700 ÷ 30 = 90

Strategy 4: Variables in the Data Set
Problem: The mean of x, x+2, and x+4 is 10. Find x.
Set up the equation: \(\frac{x + (x+2) + (x+4)}{3} = 10\)
Simplify the numerator: \(\frac{3x + 6}{3} = 10\)
Solve for x: 3x + 6 = 30
3x = 24
x = 8
 

This video gives a clear, step-by-step approach to explain how to solve mean algebra word problems.

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