SOLUTION: If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if

Question 725194: If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if the sum of ages of students in 861 .
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if the sum of ages of students in 861 .
---
a(1) = 16 years
d = 3/12 = 1/4
Sum = 861 years
--------------------
a(n) = a(1) + (n-1)d
--------------------------
S(n) = (n/2)(a(1) + a(n)
--------------
861 = (n/2)(16 + 16+(n-1)(1/4))
-------
861 = (n/2)(32 + (n-1)(1/4)
----
861 = 16n + (n^2-n)(1/8)
----
6888 = 128n + n^2-n
---
n^2 + 127n - 6888 = 0
---------------
n = 41
====================
cheers,
Stan H.
======================
RELATED QUESTIONS
[ the average age of a class of 21 students is 14 years 3 months, IF the oldest student... (answered by TimothyLamb)

You have three cousins with mean age 11. If the oldest is twice the age of the youngest... (answered by solver91311)

Julie has three children whose ages are consecutive odd integers. If x represents the... (answered by JulietG)

Three siblings have a combined age of 108. The oldest and youngest are 8 years apart.... (answered by ankor@dixie-net.com)

The ages of three men are in the ratio 3:4:5. If the difference between the ages of the... (answered by ewatrrr)

the ages of the three brothers are concecutive even integers. three time the age of the... (answered by Maths68)

The ages of three brothers are consecutive even intergers. Three time the age of the... (answered by lmeeks54)

The ages of three brothers are consecutive even integers. Three times the age of the... (answered by Maths68)

The ages of three older brothers are consecutive even integers. Three times the age of... (answered by stanbon)