SOLUTION: 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

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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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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: %284x%29%2F%286x%29 is the girl/boy ratio
:
Then %284x-6%29%2F%286x%2B6%29 = 25%2F75
same as
%284x-6%29%2F%286x%2B6%29 = 1%2F3
Cross multiply:
3(4x-6) = 6x + 6
12x - 18 = 6x + 6
12x - 6x = 6 + 18
6x = 24
x = 24%2F6
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
%2816-6%29%2F%2824%2B6%29 = 10%2F30 = 1/3 ratio girls to boys (75% boys)