2/5 of the students in a class are girls. After 4 boys leave the class and 2 girls join, exactly half of the class are girls. How many students were in the class originally?
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Worked Solution
Step 1: Let original total = T. Girls = 2T/5. Boys = 3T/5.
Step 2: After changes: girls = 2T/5 + 2, new total = T − 4 + 2 = T − 2.
Step 3: Condition (half are girls): (2T/5 + 2) / (T − 2) = 1/2.
Step 4: Cross-multiply: 2(2T/5 + 2) = T − 2 → 4T/5 + 4 = T − 2 → 4 = T − 4T/5 − 2 = T/5 − 2.
Step 5: T/5 = 6 → T = 30.
Step 6: Check: original girls = 12, boys = 18. After: 14 girls, 14 boys, total = 28. 14/28 = 1/2 ✓.
Correct answer: 30
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