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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?

 Jun 16, 2020
 #1
avatar+21955 
+1

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

 Jun 16, 2020
 #2
avatar+1130 
+1

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

 Jun 16, 2020

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