The ratio of the number of boys to girls in three classes are 7:5,3:2 and 1:1 respectively. 50% of the boys and 40% of the girls of the first class, 60% of the boys of the second class and 50% of the girls of the
third class join the sports club. There are 51 students in the sports club and 91 students who are not in the sports club from these three classes. If there are 6 more students in the second class than in the third
class, what is the total number of girls in the three classes?
Answers
Given : The ratio of the number of boys to girls in three classes are 7:5,3:2 and 1:1 respectively. 50% of the boys and 40% of the girls of the first class, 60% of the boys of the second class and 50% of the girls of the third class join the sports club.
To find : the total number of girls in the three classes
Solution:
Lat say Class 1 Students = 12A
Boys = 7A & Girls = 5A
Class 2 Students = 10B
Boys = 6B & Girls = 4B
Class 3 Students = 10B - 6
Boys = 5B-3 & Girls = 5B - 3
Total = 12A + 20B - 6
51 + 91 = 142 Total studnets
=> 12A + 20B - 6 = 142
=> 12A + 20B = 148
=> 3A + 5B = 37
Join Club = (50/100)(7A) + (40/100)5A + (60/100)6B + (50/100)(5B-3) = 51
=> 3.5A + 2A + 3.6B + 2.5B - 1.5 = 51
=> 5.5A + 6.1B = 52.5
3A + 5B = 37 => 165A + 275B = 2035
55A + 61 B = 525 => 165A + 183B = 1575
=> 92B = 460
=> B = 460/92
=> B = 5
=> A = 4
total number of girls in the three classes 5A + 4B + 5B - 3
= 5A + 9B - 3
= 5(4) + 9(5) - 3
= 20 + 45 - 3
= 62
62 girls in all three classes
Class 1 - Boys = 28 Girls = 20 = 48
Class 2 Boys = 30 Girls 20 = 50
Class 3 Boys 22 Girls 22 = 44
Join Club = 14 + 8 + 18 + 11 = 51
62 girls in all three classes
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