Candies and fractions

by Ron Angelo A. Gelacio
(Paranaque,Metro Manila,Philippines)

Ricky, Carl and Jerome have a total of n candies. Ricky ate 1/4 of the candies. Carl ate 1/3 of the remaining candies. Jerome ate 1/5 of the remaining candies.

Then they grouped the remaining candies into 4 groups. If there were 10 candies in each group,how many candies did the three have in first?



Solution


Ricky ate 1/4 of the candies



This means that Ricky ate 1/4 of n



1/4 of n = 1/4 × n = n/4



Carl ate 1/3 of the remaining candies



The remaining candies is n - n/4



n - n/4 = 4n/4 - n/4 = 3n/4



This means that Carl ate 1/3 of 3n/4



1/3 of 3n/4 = 1/3 × 3n/4 = 3n/12 = n/4



Jerome ate 1/5 of the remaining candies



The remaining candies is 3n/4 - n/4




3n/4 - n/4 = 2n/4 = n/2



This means that Jerome ate 1/5 of n/2




1/5 of n/2 = 1/5 × n/2 = n/10




Then they group n/10 into 4 groups.




This means that the remaining candies is divided by 4




n/10 divided by 4 = n/40



There are 10 candies in each group



n/40 = 10



Multiply both sides by 40



n = 10 × 40 = 400



The number of candies in each group is 400.




Since there are 4 groups, the total number of candies is 400 × 4 = 1600



Ricky ate 1/4 of 1600 or 1/4 × 1600 = 1600/4 = 400



1600 - 400 = 1200



Carl ate 1/3 of 1200 or 1/3 × 1200 = 1200/3 = 400



1200 - 400 = 800



Jerome ate 1/5 of 800 or 1/5 × 800 = 800/3 = 160



800 - 160 = 640



640 divided by 4 = 160



At the end each group had 160 candies