The ratio of the number of girls to the number of boys in a sports club is 3:6. There are 15 more boys than girls in the club. How many pupils are in the club altogether?
girls : boys = 3:6 = 1:2
let the number of girls be x
let the number of boys be 2x
2x - x = 15
x = 15
we have 15 girls and 30 girls for a total of 45 pupils
g = numbers of girls
b = number of boys
There are 15 more boys than girls mean:
b = g + 15
The ratio of the number of girls to the number of boys in a sports club is 3:6 mean:
g / b = 3 / 6
3 / 6 = 1 / 2 so:
g / b = 1 / 2
Replace b = g + 15 in this equation.
g / ( g + 15 ) = 1 / 2 Multiply both sides by 2
2 g / ( g + 15 ) = 1 Multiply both sides by g + 15
2 g = g + 15 Subtract g to both sides
2 g - g = g + 15 - g
g = 15
b = g + 15 = 15 + 15 = 30
In the club are altogether b + g pupils.
b + g = 30 + 15 = 45 pupils
To find the total number of pupils in the club, we first need to determine the number of girls and boys separately.
Let's assume the number of girls is "3x," where x is a common multiplier. Since the ratio of girls to boys is given as 3:6, the number of boys would be "6x" since there are 6 parts of boys for every 3 parts of girls.
We are also given that there are 15 more boys than girls in the club. This can be expressed as:
6x - 3x = 15
Simplifying, we have:
3x = 15
Dividing both sides by 3, we find:
x = 5
Now, we can determine the number of girls and boys.
Number of girls = 3x = 3 * 5 = 15
Number of boys = 6x = 6 * 5 = 30
Finally, to find the total number of pupils, we add the number of girls and boys together:
Total number of pupils = Number of girls + Number of boys = 15 + 30 = 45
Therefore, there are 45 pupils in the club altogether.