MATHEMATICS

JAMB 2004 - Question 43

Mathematics 2004 JAMB Past Questions - Question 43: The mean age of a group of student is 15 years .When the age of a teacher ,45 years old,is added to the age of the students,the mean of their ages becomes 18 years .Find the number of students in the group.

The mean age of a group of student is 15 years .When the age of a teacher ,45 years old,is added to the age of the students,the mean of their ages becomes 18 years .Find the number of students in the group.
A:
B:
C:
D:
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Correct Answer

B

Explanation

Let's assume there are 'n' students in the group.According to the given information, the mean age of the students is 15 years. Therefore, the sum of their ages is 15n.When the age of the teacher (45 years) is added to the sum of the students' ages, the total sum becomes 15n + 45.The new mean age of the group is 18 years. Therefore, the total sum of ages is 18 times the number of people in the group, which is (18)(n + 1).Setting up the equation:15n + 45 = 18(n + 1)Simplifying the equation:15n + 45 = 18n + 18Subtracting 15n from both sides:45 = 3n + 18Subtracting 18 from both sides:27 = 3nDividing both sides by 3:n = 9Therefore, there are 9 students in the group.