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

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== Solution == | == Solution == | ||

− | Noticing the variables and them being multiplied together, we try to find a good factorization. After trying a few, we stumble upon something in the form of < | + | Noticing the variables and them being multiplied together, we try to find a good factorization. After trying a few, we stumble upon something in the form of <cmath>(x+*)(y+*)(z+*)</cmath> where the blanks should be filled in with numbers. |

+ | Filling in as <cmath>(x+4)(y+2)(z+1)</cmath> gives <cmath>2x+4y+8z+xy+4yz+2xz+xyz</cmath>, and all parts happen to be multiples of the given equations. After substitution, we get <cmath>(x+4)(y+2)(z+1)=52</cmath>. |

## Revision as of 15:21, 7 May 2020

## Problem 30

How many distinct ordered triples satisfy the equations

## Solution

Noticing the variables and them being multiplied together, we try to find a good factorization. After trying a few, we stumble upon something in the form of where the blanks should be filled in with numbers. Filling in as gives , and all parts happen to be multiples of the given equations. After substitution, we get .