Question 1191538: The average number of boys in 1A, 1B and 1C is 18. This is 4 more than the average number of girls in the 3 rooms. 2/7 of the total number of girls are in 1C. 3/2 of the number of girls in 1B is the same as 3/7 of the total number of girls in the 3 rooms. What fraction of the total number of boys in the 3 rooms is in 1A if there are 40 pupils in 1A?
Answer by ikleyn(52779)   (Show Source):
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The average number of boys in 1A, 1B and 1C is 18.
This is 4 more than the average number of girls in the 3 rooms.
2/7 of the total number of girls are in 1C.
3/2 of the number of girls in 1B is the same as 3/7 of the total number of girls in the 3 rooms.
What fraction of the total number of boys in the 3 rooms is in 1A if there are 40 pupils in 1A?
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I will recover all needed and required consequences from the condition, step by step.
(1) The average of girls in the 3 rooms is 18-4 = 14.
(2) Hence, the total girls in the 3 rooms is 14*3 = 42.
(3) The number of girls in 1C is 2/7 of 42, i.e. 12 girls.
(4) 3/7 of the total numer of girls in the 3 rooms is 3/7 of 42, or 18.
(5) 3/2 of the number of girls in 1B is 18;
hence, the number of girls in 1B is 2/3 of 18, i.e. 12.
(6) It implies that the number of girls in 1A is 42-12-12 = 18.
(7) Since there are 40 pupils in 1A, the number of boys in 1A is 40-18 = 22.
(8) The total number of boys in all three classes is 18*3 = 54.
(9) Hence, the ratio of boys in 1A to the total boys is  =  . ANSWER
Solved.
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