The average score of a group of students is 75. When one student with a score of 95 joins the group, the new average becomes 79. How many students were in the group originally?
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Worked Solution
Step 1: Let the original number of students be n.
Step 2: Total score of original students = 75 × n.
Step 3: When the new student joins, the new total score = 75n + 95.
Step 4: The new number of students is n + 1.
Step 5: The new average is 79, so (75n + 95) / (n + 1) = 79.
Step 6: 75n + 95 = 79(n + 1)
Step 7: 75n + 95 = 79n + 79
Step 8: 95 - 79 = 79n - 75n
Step 9: 16 = 4n
Step 10: n = 16 ÷ 4 = 4.
Step 11: So, there were 4 students originally.
Answer: 4
Correct answer: 4
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