Talk:1989 AIME Problems/Problem 8
Solution 7
Subtracting the first equation from the second equation we get 
. Subtracting the second equation from the third equation gives 
. Subtracting these two equations, we get that 
. Note that we are trying to find ![\[16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7\]](http://latex.artofproblemsolving.com/d/d/7/dd72c4cce8764e0f47aa92ca271babbf10c158e8.png)
![\[=(9x_1+16x_2+25x_3+36x_4+49x_5+64_6+81x_7)+(7x_1+9x_2+11x_3+13x_4+15x_5+17x_6+19x_7)\]](http://latex.artofproblemsolving.com/3/2/8/32819d260de44dcfe7360de55cac805126742c18.png)
![\[=123+(5x_1+7x_2+9x_3+11x_4+13x_5+15x_6+17x_7+2x_1+x_2+x_3+x_4+x_5+x_6+x_7)\]](http://latex.artofproblemsolving.com/d/4/2/d42d1e7f4ba8139c75f92956a7a1a05271be051e.png)
![\[=123+111+100=\boxed{334}\]](http://latex.artofproblemsolving.com/9/f/6/9f6f79f0e29a6afcbcecdbdb3a597f308228ca55.png)
-Heavytoothpaste
