Difference between revisions of "1986 AIME Problems/Problem 4"
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== Problem == | == Problem == | ||
+ | Determine <math>\displaystyle 3x_4+2x_5</math> if <math>\displaystyle x_1</math>, <math>\displaystyle x_2</math>, <math>\displaystyle x_3</math>, <math>\displaystyle x_4</math>, and <math>\displaystyle x_5</math> satisfy the system of equations below. | ||
+ | <center><math>\displaystyle 2x_1+x_2+x_3+x_4+x_5=6</math></center> | ||
+ | <center><math>\displaystyle x_1+2x_2+x_3+x_4+x_5=12</math></center> | ||
+ | <center><math>\displaystyle x_1+x_2+2x_3+x_4+x_5=24</math></center> | ||
+ | <center><math>\displaystyle x_1+x_2+x_3+2x_4+x_5=48</math></center> | ||
+ | <center><math>\displaystyle x_1+x_2+x_3+x_4+2x_5=96</math></center> | ||
== Solution == | == Solution == | ||
− | + | {{solution}} | |
== See also == | == See also == | ||
* [[1986 AIME Problems]] | * [[1986 AIME Problems]] | ||
{{AIME box|year=1986|num-b=3|num-a=5}} | {{AIME box|year=1986|num-b=3|num-a=5}} |
Revision as of 19:52, 10 February 2007
Problem
Determine if
,
,
,
, and
satisfy the system of equations below.
![$\displaystyle 2x_1+x_2+x_3+x_4+x_5=6$](http://latex.artofproblemsolving.com/a/b/8/ab820c7ac6c3edef0bb989d92059fbc38d263ee1.png)
![$\displaystyle x_1+2x_2+x_3+x_4+x_5=12$](http://latex.artofproblemsolving.com/5/0/7/5078abc978de8c47927ba4e139a0a72ad5abea1a.png)
![$\displaystyle x_1+x_2+2x_3+x_4+x_5=24$](http://latex.artofproblemsolving.com/8/9/7/8976ad6980ddad409e011b98f18b3d9a0e16e431.png)
![$\displaystyle x_1+x_2+x_3+2x_4+x_5=48$](http://latex.artofproblemsolving.com/6/8/6/686a2b62d98be0c1221bf0ea3e75cc0375ac2cec.png)
![$\displaystyle x_1+x_2+x_3+x_4+2x_5=96$](http://latex.artofproblemsolving.com/b/a/e/baec7b4c76295d73b189a0940004cf6c3f1c3a06.png)
Solution
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See also
1986 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |