64% of the members in tennis club were girls. When more girls joined, the percentage increased by 6%.If there were 75 members at first, how many new girls joined the club?
Question
64% of the members in tennis club were girls. When more girls joined, the percentage increased by 6%.If there were 75 members at first, how many new girls joined the club?
Solution
Step 1: Find out how many girls were in the club at first.
64% of 75 members is 0.64 * 75 = 48 girls.
Step 2: Calculate the new percentage of girls in the club.
The new percentage is 64% + 6% = 70%.
Step 3: Find out the total number of members after the new girls joined.
Let's denote the total number of members after the new girls joined as X. Since 70% of X is equal to the number of girls (48 girls + new girls), we can write the equation as 0.70X = 48 + new girls.
Step 4: Solve the equation for X.
We can't solve for X yet because we don't know the number of new girls. However, we can express X (the total number of members after the new girls joined) in terms of the number of new girls. Rearranging the equation gives us X = (48 + new girls) / 0.70.
Step 5: Find out the number of new girls.
Since the total number of members can't decrease, X must be greater than or equal to 75. Therefore, (48 + new girls) / 0.70 >= 75. Solving this inequality for the number of new girls gives us new girls >= 75 * 0.70 - 48 = 52.5 - 48 = 4.5.
Since the number of new girls must be a whole number, at least 5 new girls must have joined the club.
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