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ratios

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In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 2:3.  How many students are in the class after these changes?

Jun 27, 2023

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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

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 27, 2023