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Question 251276: The ratio of boys to girls in a certain class is 2/3 If 4 more boys and 4 more girls are added to the class, the ratio of boys to girls will be 5/7 How many boys are in the original class?
a) 16 b) 20 c) 24 d) 28 e) 32
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Note: "The ratio of boys to girls is 2/3 means that out of every 5 students, 2 will be boys and three will be girls, so out of the entire class 2/5 will be boys and 3/5 will be girls."
Let x=number of boys and girls in the original class
Then (2/5)x=number of boys
And (3/5)x=number of girls
After the influx of students, the number of boys=(2/5)x+4
And the number of girls=(3/5)x+4
So, our equation to solve is:
(2/5)x+4=(5/12)(x+8) or
(2/5)x+4=(5/12)x+40/12 multiply each term by 60
24x+240=25x+200 subtract 25x and also 240 from each side
24x-25x+240-240=25x-25x+200-240 collect like terms
-x=-40 or
x=40 students originally in the class
(2/5)x=16----------number of boys originally in the class
(3/5)x=24-----number of girls originally in the class
And the ratio of 16/24=2/3
CK
16+4=(5/12)(48)
20=20
Hope this helps---ptaylor
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