SOLUTION: A lumberjack has 4n + 110 logs in a pile consisting of n layers. Each layer has two more logs than the layer directly above it. If the top layer has six logs, how many layers are t

Algebra ->  Permutations -> SOLUTION: A lumberjack has 4n + 110 logs in a pile consisting of n layers. Each layer has two more logs than the layer directly above it. If the top layer has six logs, how many layers are t      Log On


   



Question 638494: A lumberjack has 4n + 110 logs in a pile consisting of n layers. Each layer has two more logs than the layer directly above it. If the top layer has six logs, how many layers are there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the total logs in the pile of
+n+ layers with 6 logs on top seems to
be +%28n+%2B+5%29%2An+=+n%5E2+%2B+5n+
-----------------------
Since there are +4n+%2B+110+ logs in the pile,
+n%5E2+%2B+5n+=+4n+%2B+110+
+n%5E2+%2B+n+-+110+=+0+
Looking at this, I get
+%28+n+%2B+11+%29%2A%28+n+-+10+%29+=+0+
+n+=+10+ ( reject the negative result )
There are 10 layers
check:
+4n+%2B+110+=+4%2A10+%2B+110+
+4n+%2B+110+=+150+
and
+n%5E2+%2B+5n+=+100+%2B+50+
+n%5E2+%2B+5n+=+150+