2004 Indonesia MO Problems/Problem 5
Contents
Problem
Given a system of equations:
Then determine the value of 
.
Solution
Subtract the first equation from the second equation of the original to get
![\[3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 = 11\]](http://latex.artofproblemsolving.com/6/b/0/6b0494d6cd21e1f0bedc21215cdd8c966da4dfb0.png)
Subtract the second equation from the third equation of the original to get
![\[5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 = 111\]](http://latex.artofproblemsolving.com/5/d/0/5d09f68cf625565a0f2c4a202145571035dfe2b1.png)
The difference between the two above equations is
![\[2x_1 + 2x_2 + 2x_3 + 2x_4 + 2x_5 + 2x_6 + 2x_7 = 100\]](http://latex.artofproblemsolving.com/b/a/7/ba7ed6b1ee782b6b647539bd12adee8b68c3f4e5.png)
That means
![\[7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7 = 211\]](http://latex.artofproblemsolving.com/c/3/8/c388064735790bf4eb50413cfd73cd870ad0756d.png)
Adding that to the third equation of the original results in
![\[16x_1 + 25x_2 + 36x_3 + 49x_4 + 64x_5 + 81x_6 + 100x_7 = \boxed{334}\]](http://latex.artofproblemsolving.com/7/f/9/7f976ba8d8c5643373ba8d079a730083b35f25cc.png)
Note
This problem is a copy of Problem 8 from the 1989 AIME.
See Also
| 2004 Indonesia MO (Problems) | ||
| Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 6 |
| All Indonesia MO Problems and Solutions | ||
