SOLUTION: C. Logs are stacked so that each layer above the bottom layer is one less log than the previous (lower) layer. If the top layer has five logs, and there are 2840 logs in the entir

Algebra ->  Sequences-and-series -> SOLUTION: C. Logs are stacked so that each layer above the bottom layer is one less log than the previous (lower) layer. If the top layer has five logs, and there are 2840 logs in the entir      Log On


   

Question 472702: C. Logs are stacked so that each layer above the bottom layer is one less log than the previous (lower) layer. If the top layer has five logs, and there are 2840 logs in the entire stack, how many logs are in the bottom layer? Work must be done by algebra, not arithmetic/trial and error/guessing.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let k be the number of logs in the bottom layer, with



If we add 1+2+3+4 to both sides, we get





Since 5700 = 75*76, we obtain k = 75 through a guess-and-check-ish method. Note that we could use the quadratic formula to solve this, but it is rather tedious. Given that the answer is an integer, the best method would be to find two factors of 5700 that are 1 apart. Also, solving the quadratic k^2 + k - 5700 = 0 by factoring is also pointless since it reduces to the previous problem.