Difference between revisions of "1976 AHSME Problems/Problem 30"
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| + | == Problem 30 == | ||
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| + | 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> | ||
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| + | <math>\textbf{(A) }\text{none}\qquad | ||
| + | \textbf{(B) }1\qquad | ||
| + | \textbf{(C) }2\qquad | ||
| + | \textbf{(D) }4\qquad | ||
| + | \textbf{(E) }6 </math> | ||
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| + | [[1976 AHSME Problems/Problem 30|Solution]] | ||
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== Solution == | == Solution == | ||
satisfy the equations
![\[x+2y+4z=12\]](http://latex.artofproblemsolving.com/e/5/3/e53f6d4f56a9fd1f01ffe12c1a29b46a0f06c1dd.png)
![\[xy+4yz+2xz=22\]](http://latex.artofproblemsolving.com/6/a/3/6a38bcbbdb99991b176c33335bd1a64cf6e13970.png)
![\[xyz=6\]](http://latex.artofproblemsolving.com/b/6/2/b62793631f6681941ffdba570d7401ab0f39f1e9.png)
