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
Aug 09, 16 01:40 PM
Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let
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