Difference between revisions of "2008 iTest Problems/Problem 8"
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==Solution== | ==Solution== | ||
+ | 2x + 3y + 3z = 8, | ||
+ | 3x + 2y + 3z = 808, | ||
+ | 3x + 3y + 2z = 80808, | ||
+ | |||
+ | The Solution can be found by summing the three equations to get: | ||
+ | |||
+ | 8x + 8y + 8z = 81624 | ||
+ | |||
+ | then solving for x+y+z, divide by 8 to get: | ||
+ | |||
+ | 10,203. | ||
==See also== | ==See also== |
Revision as of 00:28, 5 August 2014
Problem
(story eliminated)
Given the system of equations
![$2x + 3y + 3z = 8$](http://latex.artofproblemsolving.com/b/1/a/b1a949a0479b1c302babf706cac5b421735369c9.png)
,
![$3x + 3y + 2z = 80808$](http://latex.artofproblemsolving.com/5/7/e/57e194550059b7d7a487e6beac99396feca762ea.png)
find .
Solution
2x + 3y + 3z = 8, 3x + 2y + 3z = 808, 3x + 3y + 2z = 80808,
The Solution can be found by summing the three equations to get:
8x + 8y + 8z = 81624
then solving for x+y+z, divide by 8 to get:
10,203.