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At a gathering, 1/3 of the people at the gathering are adults. The remaining group of people is divided into boys and girls in the ratio of 5:7. Each boy is given 2 keychains and each girl is given 5 keychains. Each accompanying adult receives 6 keychains. Given that only 368 keychains are given away to boys and adults, how many more children are there than adults?

 Jul 4, 2022
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Let the total number  of people  =  N

 

(1/3)N are adults

 

(2/3)N are boys and girls

 

Of this  (5/12)(2/3)N are boys =  (10/36)N  = (5/18)N     

A nd (7/12)(2/3)N are girls =   (14/36) N =  (7/18)N

 

Note (1/3)N  =(6/18) N

 

No. boys * no. of keychains rec'd  + No. adults * keychains rec'd =  368

 

So

 

(5/18)N* 2 +  (6/18) N * 6 =  368

 

(10/18)N  + (36/18)N =  368

 

46N / 18  =  368

 

23N / 9 = 368

 

(368 * 9 )  / 23 =  N =   144

 

No. of chldren = (2/3) 144 =  96

 

No. of adults =  48

 

96 - 48 =    

 

48 more 

 

 

cool cool cool

 Jul 4, 2022

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