Question
The average weight of a certain number of students in a
group was 72 kg. If 11 students, with an average weight of 76 kg each, leave the group, and 5 students, each with an average weight of 79 kg, join the group, the average weight of the students in the group decreases by 0.6 kg. The number of students initially in the group was:Solution
Let: Initial students = x Initial total = 72x 11 leave (76 kg avg) ⇒ lose 836 kg 5 join (79 kg avg) ⇒ gain 395 kg New total = 72x − 836 + 395 = 72x − 441 New students = x − 6 New avg = 72 − 0.6 = 71.4 Equation: (72x − 441)/(x − 6) = 71.4 → 72x − 441 = 71.4(x − 6) → 72x − 441 = 71.4x − 428.4 → 0.6x = 12.6 ⇒ x = 21
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