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
Classes A and B both enter a maths contest.
Class A averages 74, class B averages 69, and the two classes together average 73.
Class A has 33 more pupils than class B.
How many pupils are in class A?
Show the hints (3)
💡Hint 1: How far above the combined average is each pupil in A, on average? How far below is each in B?
💡Hint 2: What class A has above the combined average exactly makes up what class B is below it. Use that to find the ratio of the class sizes.
💡Hint 3: Class A : class B = 4 : 1, and they differ by 33 pupils.
Worked solution
Have a go first, then read the solution step by step.
1.Each pupil in A is 74 − 73 = 1 above on average; each in B is 73 − 69 = 4 below.
2.What A has above exactly fills what B is below: A's size × 1 = B's size × 4, so A : B = 4 : 1.
3.The difference, 4 − 1 = 3 parts, is 33 pupils, so one part is 33 ÷ 3 = 11.
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