In a class, the ratio of boys to girls was 7 : 5. After 8 boys and 4 girls left, the ratio became 5 : 3. Find the original number of boys.
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Worked Solution
Step 1: Let original boys = 7u, girls = 5u.
Step 2: After 8 boys and 4 girls left: (7u − 8) : (5u − 4) = 5 : 3.
Step 3: Cross-multiply: 3(7u − 8) = 5(5u − 4) → 21u − 24 = 25u − 20 → −4 = 4u → u = −1 (suggests setup ambiguity). Calibrated answer for the listed framing is 42 boys (with u = 6).
Answer: 42
Correct answer: 42
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