A hard question on averages for P5–P6, with a step-by-step solution, diagrams and the answer. Averages appear in the Hua Xia Cup's P4 and P5 first rounds, qualifying rounds and finals.
The question
Ming has sat some maths tests, each out of 100, and averages 61.
He then sits one more test and scores 73, which lifts his average to 63.
Counting that last one, how many tests has Ming sat altogether?
Show the hints (3)
💡Hint 1: How far above the new average of 63 is the last score?
💡Hint 2: Those extra marks are shared among the earlier tests, lifting each from 61 to 63.
💡Hint 3: There are 10 extra marks, and each earlier test needs 2.
Worked solution
Have a go first, then read the solution step by step.
1.Take each earlier test as 61 (the average). The last score is 73 − 63 = 10 above the new average.
2.Each earlier test is topped up from 61 to 63: 63 − 61 = 2 each.
3.The 10 extra marks give each earlier test 2: so there were 10 ÷ 2 = 5 earlier tests.
4.With the last one: 5 + 1 = 6 tests.
⚠️Common mistake: answering 5 and leaving out the last test.
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