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?

Guest Jul 4, 2022

#1**+1 **

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

CPhill Jul 4, 2022