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Question 277964: Mr. Smith has three times as many girls as boys in his class. Ms. Perry has twice as many boys as girls in her class. Mr. Smith has 60 students in his class and Ms. Perry has 45 students. If the classes are combined into one class, the ratio of boys to girls is:
(A) 3 : 4 (B) 4 : 3 (C) 5 : 4 (D) 4 : 5 (E) 3 : 2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let b = number of boys
let g = number of girls.
In Mr. Smith's class, g = 3*b
In Ms. Perry's class, b = 2*g
Mr. smith has 60 students in his class.
Ms. Perry has 45 students in her class.
Combine the classes and what is the ratio of boys to girls?
in Mr. Smith's class, you have:
b + g = 60
Since g = 3*b, you get:
b + 3*b = 60 which becomes:
4*b = 60 which becomes:
b = 15
You have 15 boys and 45 girls in Mr. Smith's class.
The number of girls is 3 * the number of boys which is correct.
In Ms. Perry's class, you have:
b + g = 45
Since b = 2*g, this becomes:
2*g + g = 45 which becomes:
3*g = 45 which becomes:
g = 15
Ms. Perry has 30 boys and 15 girls.
The number of boys is 2 * the number of girls which is correct.
So, you have:
15 boys and 45 girls in Mr. Smith's class.
30 boys and 15 girls in Ms. Perry's class.
When you combine the classes, you have:
45 boys and 60 girls for a total of 105 students.
The ratio of boys to girls is equal to:
45/60 = .75
That would be the same as 3:4 which is selection A.
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