In a P6 cohort fitness test, the average mass of $6$ boys is $45$ kg. The HEAVIEST boy weighs $60$ kg. The remaining $5$ boys have an average mass that exceeds the LIGHTEST boy's mass by $5$ kg. Find the mass of the lightest boy.
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Worked Solution
Step 1: Use the relationship $\text{total} = \text{average} \times \text{count}$ to find the total mass of all 6 boys: $6 \times 45 = 270$ kg.\n
Step 2: Remove the heaviest boy from the total to focus on the OTHER 5 boys: total of the 5 remaining boys = $270 - 60 = 210$ kg.\n
Step 3: Find the average mass of these 5 boys: $210 \div 5 = 42$ kg.\n
Step 4: The question states that this 5-boy average EXCEEDS the lightest boy's mass by 5 kg. So the lightest boy's mass = (5-boy average) − 5 = $42 - 5 = 37$ kg.\nCheck: lightest = 37 → 5-boy average = 37 + 5 = 42 → 5-boy total = 5 × 42 = 210 → cohort total = 210 + 60 = 270 → cohort average = 270 ÷ 6 = 45 kg ✓.
Answer: 37 kg
Correct answer: 37 kg
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