SOLUTION: You have 9 logs to form a triangle. The bottom row is 4, then 3 then 2 = 9 logs. What is the amount on the bottom row if you have 2015 logs?

Algebra ->  Triangles -> SOLUTION: You have 9 logs to form a triangle. The bottom row is 4, then 3 then 2 = 9 logs. What is the amount on the bottom row if you have 2015 logs?       Log On


   



Question 981967: You have 9 logs to form a triangle. The bottom row is 4, then 3 then 2 = 9 logs.
What is the amount on the bottom row if you have 2015 logs?

Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You have 9 logs to form a triangle. The bottom row is 4, then 3 then 2 = 9 logs.
What is the amount on the bottom row if you have 2015 logs?
-----------
1000, 1000 & 15 will make a triangle.
======================================
***

Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor doesn't have a clue as to what you want.

Starting at the top row with 2 logs, then three logs, etc., it's
 
2%2B3%2B4%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2Ba%5Bn%5D%22%22=%22%222015
 
S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29%5D%29
 
S%5Bn%5D=2015, a%5B1%5D=2, d=1
 
2015%22%22=%22%22expr%28n%2F2%29%282%282%29%5E%22%22%2B%28n-1%29%5E%22%221%29
 
2015%22%22=%22%22expr%28n%2F2%29%284%2Bn-1%29
 
2015%22%22=%22%22expr%28n%2F2%29%283%2Bn%29
 
Multiply both sides by 2 to clear the fraction:
 
4030 = n(3+n)
 
4030 = 3n+n²
 
0 = n²+3n-4030
 
To factor that we have to find two integers that
multiply to give 4030 and have a difference of 3.
That's such a small difference in comparison to 4030
they would have to both be near the square root of 
4030 which is about 63.5.  63 doesn't go evenly into 
4030, but 62 does. so 62×65=4030 so it factors this
way:
 
0 = (n-62)(n+65)
 
n-62 = 0   n+65 = 0
   n = 62     n = -65   <-- ignore since negative

So there are 62 rows of logs.  The bottom row of logs
has as many logs as the 62nd term. 

Now we find what the 62nd term is

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

a%5B62%5D%22%22=%22%222%2B%2862-1%291

a%5B62%5D%22%22=%22%222%2B61

a%5B62%5D%22%22=%22%2263 logs.
 
Edwin