Question

On the first day of school, the percentage of boys in a particular class is 60%. During the school year six girls move away and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school

Answer 1

24 boys 16 girls

Answer 2

6 boys = 15%
40 students = 100%

Answer 3

Thanks sorry i stepped away! How did you set the equation up ??

Answer 4

x... girls at 1st day.
y... boys at 1st day.
\[\frac{y}{x+y}=0.6\]
... boys percentage at 1st day.
\[\frac{y+6}{x-6+y+6}=\ 0.75\]
...boys percentage after replacing.
So you must solve this equation system.
\[\frac{y}{x+y}=\frac{3}{5}\]
\[\frac{y+6}{x+y}=\frac{3}{4}\]
Find x from 1st equation:
\[x=\frac{5y-3y}{3}=\frac{2y}{3}\]
Put it in 2nd equation to find y:
\[\frac{y+6}{\frac{2y}{3}+y}=\frac{3}{4}\]
\[y=24\]
And find the x:
\[x=\frac{2\times 24}{3}=16\]
So answer is that at 1st day there was 16 girls and 24 boys in the class.