For every boy taking classes at the music school, there are 3 girls who are taking classes at the school. If there 128 students taking classes, write and solve a proportion to predict the number of girls taking classes at the school.
To solve this problem, we can set up a proportion to find the number of girls taking classes at the school.
Let's assign the variable "x" to represent the number of boys.
According to the given information, we know that for every boy taking classes, there are 3 girls taking classes. Therefore, we can say that the ratio of boys to girls is 1:3.
So, the number of girls (G) can be found by multiplying the number of boys (x) by the ratio of boys to girls (1/3):
G = (1/3) * x
Now, we are told that there are a total of 128 students taking classes at the school. This includes both boys and girls. Therefore, the sum of the number of boys (x) and the number of girls (G) should equal 128:
x + G = 128
Now, substitute the expression for G from the first equation into the second equation:
x + (1/3) * x = 128
Multiply through by 3 to remove the fraction:
3x + x = 384
Combine like terms:
4x = 384
Divide both sides by 4 to solve for x:
x = 96
Now, substitute this value of x back into the equation for G:
G = (1/3) * 96
G = 32
Therefore, there are 32 girls taking classes at the school.
boy : girls = 1 : 3 or x : 3x
x + 3x = 128
4x = 128
x = 32
so 32 girls and 3x or 96 girls take music
or
3/4 = n/128 , where n is the number of girls
4n = 384
n= 384/4 = 96