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The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?
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Given information:
- The age of the youngest boy is 8 years.
- The ages of the rest of the participants have a common difference of 4 months.
- The sum of the ages of all the participants is 168 years.
Calculating the number of participants:
To find the age of the eldest participant, we first need to determine how many participants there are in total. We can do this by finding the common difference of the ages and calculating the number of terms in the arithmetic sequence.
Let's assume the number of participants is 'n' (including the youngest boy). The age of the youngest boy is 8 years, so the second participant would be 8 + 4 months, the third participant would be 8 + 8 months, and so on.
We can represent the ages of the participants as an arithmetic sequence:
8, 8 + 4 months, 8 + 8 months, 8 + 12 months, ...
The nth term of an arithmetic sequence can be found using the formula:
an = a + (n - 1)d
In this case, a = 8 years (or 96 months) and d = 4 months. We need to find the value of n when the sum of the ages of all participants is 168 years (or 2016 months).
Calculating the sum of ages:
The sum of an arithmetic sequence can be calculated using the formula:
Sn = (n/2)(2a + (n - 1)d)
In this case, the sum of the ages is given as 168 years (or 2016 months). Plugging in the values, we have:
2016 = (n/2)(2*96 + (n - 1)*4)
Simplifying the equation:
2016 = (n/2)(192 + 4n - 4)
2016 = (n/2)(188 + 4n)
4032 = n(188 + 4n)
Simplifying further, we get a quadratic equation:
4n^2 + 188n - 4032 = 0
Solving the quadratic equation:
Using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 188, and c = -4032. Plugging in the values, we can solve for n.
After calculating, we find that n = 9 or n = -47/2. Since the number of participants cannot be negative, we discard the negative value.
Therefore, there are 9 participants in total, including the youngest boy.
Calculating the age of the eldest participant:
Now that we know there are 9 participants, we can find the age of the eldest participant by adding the common difference to the age of the youngest boy 8 times.
The age of the eldest participant = 8 years + 8 * 4 months
Converting months to years, we get:
8 + (8 * 4) / 12 = 10 and 2/3 years
Therefore, the age of the eldest participant in the painting competition is 10 years and 8 months.
- The age of the youngest boy is 8 years.
- The ages of the rest of the participants have a common difference of 4 months.
- The sum of the ages of all the participants is 168 years.
Calculating the number of participants:
To find the age of the eldest participant, we first need to determine how many participants there are in total. We can do this by finding the common difference of the ages and calculating the number of terms in the arithmetic sequence.
Let's assume the number of participants is 'n' (including the youngest boy). The age of the youngest boy is 8 years, so the second participant would be 8 + 4 months, the third participant would be 8 + 8 months, and so on.
We can represent the ages of the participants as an arithmetic sequence:
8, 8 + 4 months, 8 + 8 months, 8 + 12 months, ...
The nth term of an arithmetic sequence can be found using the formula:
an = a + (n - 1)d
In this case, a = 8 years (or 96 months) and d = 4 months. We need to find the value of n when the sum of the ages of all participants is 168 years (or 2016 months).
Calculating the sum of ages:
The sum of an arithmetic sequence can be calculated using the formula:
Sn = (n/2)(2a + (n - 1)d)
In this case, the sum of the ages is given as 168 years (or 2016 months). Plugging in the values, we have:
2016 = (n/2)(2*96 + (n - 1)*4)
Simplifying the equation:
2016 = (n/2)(192 + 4n - 4)
2016 = (n/2)(188 + 4n)
4032 = n(188 + 4n)
Simplifying further, we get a quadratic equation:
4n^2 + 188n - 4032 = 0
Solving the quadratic equation:
Using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 188, and c = -4032. Plugging in the values, we can solve for n.
After calculating, we find that n = 9 or n = -47/2. Since the number of participants cannot be negative, we discard the negative value.
Therefore, there are 9 participants in total, including the youngest boy.
Calculating the age of the eldest participant:
Now that we know there are 9 participants, we can find the age of the eldest participant by adding the common difference to the age of the youngest boy 8 times.
The age of the eldest participant = 8 years + 8 * 4 months
Converting months to years, we get:
8 + (8 * 4) / 12 = 10 and 2/3 years
Therefore, the age of the eldest participant in the painting competition is 10 years and 8 months.
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The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?
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The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?.
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?.
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