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Test scores — a sixth student joins the group
The average score of 5 students is 72. A sixth student joins and the new average becomes 74. What is the sixth student's score?
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The pattern behind it: An average is a total
Turn the average back into a total before doing anything with it.
In this one. The sixth score is not just the new average — it is the new average plus the lift it has to hand to each of the other five: 74 + 5 x 2 = 84.
How to spot it
The word 'average' appears alongside a group being split into two parts, or two separate journeys or trips being combined into one overall figure.
Common mistake
Children average two averages directly, such as averaging two speeds or two group averages, without weighting by how many, or how long, each part actually covers.
Try one like it
Standard A bakery's week — average daily sales A bakery recorded its sales over 5 days: $42, $48, $55, $51 and $44. What was the average daily sales amount over the 5 days?The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.