In Linguistics 101, the ratio of the number of girls to the number of boys is $3:2$. When seven more girls join the class, and two boys drop the class, the ratio of the number of girls to the number of boys becomes $5:2$. How many students are in the class after these changes?
Let 3x be the number of girls
and 2x be the number of boys.
Seven more girls join the class: the number of girls is now 3x + 7
Two boys drop the class: the number of boys is now 2x - 2.
The ratio of girls to boys is now 5:2 ---> (3x + 7) : (2x - 2) = 5 : 2
(3x + 7) / (2x - 2) = 5 / 2
2 · (3x + 7) = 5 · (2x - 2)
6x + 14 = 10x - 10
24 = 4x
6 = x
Current number of girls: 3x + 7 ---> 3(6) + 7 = 25
Current number of boys: 2x - 2 ---> 2(6) - 2 = 10
so we need a common denominator by the ratios meet the requierments so e make variables b and g for boys and girls so we have g/b=3/2 and (g+7)/(b-2)=5/2 so we can Substitute the b into 2/3 g to get (g+7)/(2/3(g-2))=5/2 or we can simplify it into (((3/2)b)+7)/b-2=5/2 so we have g=18 and b=12 so then we have g+7=25 and b-2=10 then we do 25+10=35 and the number of students are in the class after these changes are 35