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Author:
reymxia
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3Given,
The student's ages are in A.P.
The common difference = 3 months.
The younger student's age = 12.
The total age = 375yrs.
To Find,
The count of students in the group.
Solution,
Given that,
The ages of students are in A.P.
The difference between their ages = 3months.
3/12 = 1/4yrs
The total of their age = 375yrs.
Younger one's age =12yrs.
In A.P, the sum of the terms
S = n/2 (2a +(n-1)d)
a =12.
S = n/2 (2*12+ (n-1)1/4)
S = 375
n/2(2*12+(n-1)1/4) = 375
n/2(24+(n-1)1/4) = 375
n(24+(n-1)1/4) = 750
n(24*4+(n-1)) = 750 * 4
n(96+(n-1)) = 3000
96n + [tex]n^{2}[/tex] -n = 3000
95n + [tex]n^{2}[/tex] = 3000
[tex]n^{2}[/tex] + 95n -3000 = 0
Let's factorise it.
[tex]n^{2}[/tex] + 120n -25n -3000 = 0
n(n+120) -25(n +120) = 0
So,
n = -120 or 25
Hence, 25is the total number of students in the group.
Author:
gilliant8vr
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