Difference between revisions of "2005 iTest Problems/Problem 10"

Revision as of 17:26, 13 October 2025

@@ Line 1: / Line 1: @@
-==Solution 1==
-Let <math>x = \frac{43 - 22y}{21}</math> such that <math>1 < \frac{43 - 22y}{21} < 11</math>. This means that <math>-\frac{94}{11} < y < 1</math>. If <math>y \in \mathbb{Z}</math>, then <math>y ={-8,-7,-6,-5,-4,-3,-2,-1,0}</math>. However, none of these values for <math>y</math> results in a complementary integral value for <math>x</math>. Therefore, there are <math>\boxed{0}</math> integer solutions <math>x, y \in \mathbb{Z}</math> that solves <math>21x + 22y = 43</math> over <math>1 < x < 11</math> and <math>y < 22</math>.
 ==See Also==
 {{iTest box|year=2005|num-b=9|num-a=11}}