The computer club had ¾ as many members as the drama club. After half the drama club members left to join the computer club, the computer club had 27 more members than the drama club. How many members did the drama club have at first?
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Let's solve this problem step by step.
Let's assume the number of members in the drama club at first is "x". Given that the computer club had ¾ as many members as the drama club, we can say that the computer club had (3/4)x members initially.
After half the drama club members left to join the computer club, the drama club will have (1/2)x members remaining, and the computer club will have (3/4)x + (1/2)x members.
We are also given that the computer club had 27 more members than the drama club after this change. So we can write the equation:
(3/4)x + (1/2)x = (1/2)x + 27
To simplify the equation, we can multiply everything by 4 to remove the fractions:
3x + 2x = 2x + 108
Combining like terms:
5x = 2x + 108
Subtracting 2x from both sides:
3x = 108
Dividing both sides by 3:
x = 36
Therefore, the drama club had 36 members at first.