The average weight of a certain number of students in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weight of 80 kg join the group, the average weight of the students in the decreases by 0.7 kg. The number of students initially in the group is?
Question
The average weight of a certain number of students in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weight of 80 kg join the group, the average weight of the students in the decreases by 0.7 kg. The number of students initially in the group is?
Solution
Let's denote the initial number of students as 'x'.
According to the problem, the total weight of these 'x' students is 72x kg.
When 10 students leave, the total weight becomes 72x - 10*78 kg.
When 4 students join, the total weight becomes 72x - 1078 + 480 kg.
The new average weight is 72 - 0.7 = 71.3 kg.
So, we can set up the equation: (72x - 1078 + 480) / (x - 10 + 4) = 71.3
Solving this equation will give us the initial number of students 'x'.
Let's simplify the equation:
(72x - 780 + 320) / (x - 6) = 71.3
(72x - 460) / (x - 6) = 71.3
Cross-multiplying gives us:
72x - 460 = 71.3x - 427.8
Subtract 71.3x from both sides:
0.7x = 32.2
Finally, divide both sides by 0.7 to solve for 'x':
x = 32.2 / 0.7
x = 46
So, the initial number of students in the group was 46.
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