Difference between revisions of "1976 AHSME Problems/Problem 30"

Line 1: Line 1:
 +
== Problem 30 ==
 +
 +
How many distinct ordered triples <math>(x,y,z)</math> satisfy the equations
 +
<cmath>x+2y+4z=12</cmath>
 +
<cmath>xy+4yz+2xz=22</cmath>
 +
<cmath>xyz=6</cmath>
 +
 +
 +
<math>\textbf{(A) }\text{none}\qquad
 +
\textbf{(B) }1\qquad
 +
\textbf{(C) }2\qquad
 +
\textbf{(D) }4\qquad
 +
\textbf{(E) }6  </math>
 +
 +
[[1976 AHSME Problems/Problem 30|Solution]]
 +
 +
 
== Solution ==
 
== Solution ==

Revision as of 14:04, 7 May 2020

Problem 30

How many distinct ordered triples $(x,y,z)$ satisfy the equations \[x+2y+4z=12\] \[xy+4yz+2xz=22\] \[xyz=6\]


$\textbf{(A) }\text{none}\qquad \textbf{(B) }1\qquad \textbf{(C) }2\qquad \textbf{(D) }4\qquad \textbf{(E) }6$

Solution


Solution

Invalid username
Login to AoPS