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
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.