A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?
Practice Questions
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Q1
A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?
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Total score = 65 * n + 85. New average = (65n + 85) / (n + 1).
Questions & Step-by-step Solutions
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Q
Q: A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?
Solution: Total score = 65 * n + 85. New average = (65n + 85) / (n + 1).
Steps: 7
Step 1: Understand that the average score of the class is 65. This means if there are 'n' students, the total score of all students is 65 times 'n'.
Step 2: Calculate the total score of the class before the new student joins. This is done by multiplying the average score (65) by the number of students (n). So, total score = 65 * n.
Step 3: A new student joins the class with a score of 85. Now, we need to add this score to the total score we calculated in Step 2.
Step 4: The new total score becomes 65 * n + 85.
Step 5: The class size increases by one because of the new student. So, the new number of students is n + 1.
Step 6: To find the new average score, we divide the new total score (65 * n + 85) by the new number of students (n + 1).
Step 7: The formula for the new average is (65 * n + 85) / (n + 1).
