Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 21, 2011"
m (→Solution) |
m (→Solution) |
||
Line 16: | Line 16: | ||
<math>x=2y</math> | <math>x=2y</math> | ||
− | + | Then we just plug this back into the original parameter, where <math>z=1002001</math>. | |
− | + | <math>a(2y)+by=1002001</math> | |
+ | <math>2ay+by=1002001</math> | ||
+ | <math>y(2a+b)=1002001</math> | ||
+ | <math>y=\frac{1002001}{2a+b}</math> | ||
+ | <math>=\frac{143}{53}</math> | ||
− | + | Then this also means that <math>x=\frac{286}{106}</math> |
Revision as of 16:02, 21 July 2011
Problem
AoPSWiki:Problem of the Day/July 21, 2011
Solution
Note: someone check the arithmetic please
For purposes of generalization, let the equations be and
. Notice that
. Swap this out for a new variable
.
This gives
.
Multiply the left equation by two and substitute it into the other equation.
, which implies that
. Substituting the actual numbers back in gives:
Simplifying:
Which further simplifies to:
Then we just plug this back into the original parameter, where .
Then this also means that