SOLUTION: A boy has 231 marbles. he arranges them in rows so that each row contains on e marble less than the preceding. the last row consist of one marble only, which forms the vertex of a

Question 913235: A boy has 231 marbles. he arranges them in rows so that each row contains on e marble less than the preceding. the last row consist of one marble only, which forms the vertex of a triangle. how many marbles are there in the base of the triangle?
Found 2 solutions by mananth, richwmiller:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A boy has 231 marbles. he arranges them in rows so that each row contains on e marble less than the preceding. the last row consist of one marble only, which forms the vertex of a triangle. how many marbles are there in the base of the triangle?

The arrangement is in Arithmetic progression

a= 1
d=1
total marbles = 231
Sn = 231
Sn = n/2(2a+(n-1)d)
231= n/2(2+(n-1)1)
231*2 = n(n+1)
n^2+n=462
n^2+n-462=0
n^2+22n-21n-462=0
n(n+22)-21(n+22)=0
(n-21)(n+22)=0
n= 21 OR -22
ignore negative
n= 21 number of rows
tn = a+(n-1)d
t21 = 1+(21-1)1
t20 = 21
21 marbles on the base line
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!

a21 = 21
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