There are 5 children. All five children are born at an interval of 3 years which means that the difference between consecutive children is 3 years. The sum age of all the children is 60 years. What is the age of the oldest child?
Question
There are 5 children. All five children are born at an interval of 3 years which means that the difference between consecutive children is 3 years. The sum age of all the children is 60 years. What is the age of the oldest child?
Solution
To solve this problem, we can use the formula for the sum of an arithmetic series.
The sum S of an arithmetic series is given by the formula S = n/2 * (a + l) where n is the number of terms, a is the first term (age of the youngest child), and l is the last term (age of the oldest child).
We know that the sum of the ages of the children is 60 years and there are 5 children. So, we have:
60 = 5/2 * (a + l)
This simplifies to:
120 = 5 * (a + l)
Further simplification gives:
24 = a + l
We also know that the difference between the ages of consecutive children is 3 years. Since there are 5 children, the difference between the age of the oldest and youngest child is 3 * 4 = 12 years.
So, we have:
l = a + 12
Substituting this into the first equation gives:
24 = a + a + 12
Solving for a gives:
a = 6
Substituting a = 6 into the equation l = a + 12 gives:
l = 6 + 12 = 18
So, the oldest child is 18 years old.
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