A medium question on averages for P5, 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 sat four maths tests, each marked out of 100.
He scored 72, 83 and 72 in the first three.
His average over all four is 75.
What did he score in the fourth test?
Show the hints (2)
💡Hint 1: Average × number of tests = total. What is the total for four tests?
💡Hint 2: Take away the first three scores to leave the fourth.
Worked solution
Have a go first, then read the solution step by step.
1.An average of 75 is as if all four tests scored 75. Total for four tests: 75 × 4 = 300.
2.First three: 72 + 83 + 72 = 227.
3.The total less the first three leaves the fourth: 300 − 227 = 73.
⚠️Common mistake: taking the average of the first three as the fourth score.
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