Difference between revisions of "1986 AIME Problems/Problem 4"
Baijiangchen (talk | contribs) m (→Solution) |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | Determine <math> | + | Determine <math>3x_4+2x_5</math> if <math>x_1</math>, <math>x_2</math>, <math>x_3</math>, <math>x_4</math>, and <math>x_5</math> satisfy the system of equations below. |
| − | <center><math> | + | <center><math>2x_1+x_2+x_3+x_4+x_5=6</math></center> |
| − | <center><math> | + | <center><math>x_1+2x_2+x_3+x_4+x_5=12</math></center> |
| − | <center><math> | + | <center><math>x_1+x_2+2x_3+x_4+x_5=24</math></center> |
| − | <center><math> | + | <center><math>x_1+x_2+x_3+2x_4+x_5=48</math></center> |
| − | <center><math> | + | <center><math>x_1+x_2+x_3+x_4+2x_5=96</math></center> |
== Solution == | == Solution == | ||
| Line 17: | Line 17: | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 19:04, 4 July 2013
Problem
Determine 
if 
, 
, 
, 
, and 
satisfy the system of equations below.
Solution
Adding all five equations gives us 
so 
. Subtracting this from the fourth given equation gives 
and subtracting it from the fifth given equation gives 
, so our answer is 
.
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 | ||
- AIME Problems and Solutions
- American Invitational Mathematics Examination
- Mathematics competition resources
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
