There were 20% more boys than girls in a swimming club. After 50 girls left, there were twice as many boys as girls in the club. How many boys were there in the club?
Solve the equtions b = 1.2g and b= 2(g-50) to get 150 boys.
To solve this problem, we can use algebraic equations.
Let's say the initial number of girls in the swimming club is represented by "G" and the number of boys is represented by "B".
Based on the given information, we know that there were initially 20% more boys than girls. Mathematically, this can be expressed as:
B = G + 0.2G
Simplifying this equation, we get:
B = 1.2G
Next, it is mentioned that after 50 girls left the club, there were twice as many boys as girls. So, after the girls left, the number of boys would be twice the number of girls minus 50. Mathematically, this can be expressed as:
B - 50 = 2(G - 50)
Expanding and simplifying this equation, we get:
B - 50 = 2G - 100
B = 2G - 50
Now we have two equations:
B = 1.2G (equation 1)
B = 2G - 50 (equation 2)
To find the number of boys, we can substitute equation 2 into equation 1:
2G - 50 = 1.2G
Subtracting 1.2G from both sides:
0.8G = 50
Dividing both sides by 0.8:
G = 62.5
Since the number of students cannot be a fraction, we can assume that there were 62 girls in the swimming club initially.
Substituting this back into equation 1:
B = 1.2 * 62
B = 74.4
Since the number of students cannot be a fraction, we round down to the nearest whole number.
Therefore, there were approximately 74 boys in the club.