80% of the members in a badminton club were male and the rest were female.after 450 members left the club,the number of male members was decreased by 25% and the number of female members was decreased by 50%.find the mumber of members in the badminton club at first.
X members at first.
0.8 * x = 0.8x Male.
x - 0.8x = 0.2x Female.
After 450 members left:
0.75*0.8x + 0.5*0.2x = x-450.
0.6x + 0.1x - x = -450, X = 1500.
To find the number of members in the badminton club at the beginning, we'll need to follow the steps below:
Step 1: Let's assume the total number of members in the badminton club at the beginning was "x."
Step 2: Given that 80% of the members were male, the number of male members would be 0.8x (80% is the same as 0.8).
Step 3: Since the rest of the members were female, the number of female members would be (1 - 0.8)x, which simplifies to 0.2x.
Step 4: After 450 members left the club, the new number of male members would be 0.75 times the original number of male members (a 25% decrease). Therefore, the new number of male members would be 0.75 * 0.8x.
Step 5: After 450 members left, the new number of female members would be 0.5 times the original number of female members (a 50% decrease). Therefore, the new number of female members would be 0.5 * 0.2x.
Step 6: The total number of members remaining after the departure of 450 members would be the sum of the new number of male members and the new number of female members, which can be expressed as:
0.75 * 0.8x + 0.5 * 0.2x
Step 7: According to the problem statement, this total number of remaining members is equal to 450 (as stated after the 450 members left). So we can set up the equation:
0.75 * 0.8x + 0.5 * 0.2x = 450
Step 8: Simplifying the equation:
0.6x + 0.1x = 450
0.7x = 450
Step 9: Solving for x:
x = 450 / 0.7
Step 10: Calculating x:
x = 642.857
The number of members in the badminton club at the beginning was approximately 643.