1. A playschool contains 4 boys and y girls. On every Wednesday during winter, five students, of which at least three are boys, go to Zoological Garden, a different group being sent every week. At the Zoological Garden, each boy in the group is given a ball. If the total number of balls distributed is 368, then the value of y is
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By: anil on 05 May 2019 02.39 am
Total 5 students out of 4 boys and y girls can be chosen in two ways : (1) 3 Boys and 2 Girls = $$4c_{3}*$$y$$c_{2}$$ (2) 4 Boys and 1 Girls = $$4c_{4}*$$y$$c_{1}$$
So total number of balls given to boys : 3*$$4c_{3}*$$y$$c_{2}$$+4*$$4c_{4}*$$y$$c_{1}$$ = 368 $$6(y)(y-1)+4y$$ = 368
6$$y^{2}-2y-368$$ = 0
3$$y^{2}-y-184$$ = 0
$$(y-8)(3y+23)$$ = 0 $$y=8$$, y $$ eq$$ $$ frac{-23}{3}$$
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So total number of balls given to boys : 3*$$4c_{3}*$$y$$c_{2}$$+4*$$4c_{4}*$$y$$c_{1}$$ = 368 $$6(y)(y-1)+4y$$ = 368
6$$y^{2}-2y-368$$ = 0
3$$y^{2}-y-184$$ = 0
$$(y-8)(3y+23)$$ = 0 $$y=8$$, y $$
eq$$ $$ frac{-23}{3}$$