Question 230815
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.
:
Let x = the multiplier
:
Use the ratio method
Originally: {{{(4x)/(6x)}}} is the girl/boy ratio
:
Then {{{(4x-6)/(6x+6)}}} = {{{25/75}}}
same as
{{{(4x-6)/(6x+6)}}} = {{{1/3}}}
Cross multiply:
3(4x-6) = 6x + 6
12x - 18 = 6x + 6
12x - 6x = 6 + 18
6x = 24
x = {{{24/6}}}
x = 4 is the multiplier
then
4*4 = 16 girls on the 1st day of school
and
4*6 = 24 boys
;
:
Check when 6 girls leave and 6 boys arrive
{{{(16-6)/(24+6)}}} = {{{10/30}}} = 1/3 ratio girls to boys (75% boys)