2005 iTest Problems/Problem 16

Problem

How many distinct integral solutions of the form $(x, y)$ exist to the equation $21x + 22y = 43$ such that $1 < x < 11$ and $y < 22$ ?

Solution 1

Let $x = \frac{43 - 22y}{21}$ such that $1 < \frac{43 - 22y}{21} < 11$ . This means that $-\frac{94}{11} < y < 1$ . If $y \in \mathbb{Z}$ , then $y ={-8,-7,-6,-5,-4,-3,-2,-1,0}$ . However, none of these values for $y$ results in a complementary integral value for $x$ . Therefore, there are $\boxed{0}$ integer solutions $x, y \in \mathbb{Z}$ that solves $21x + 22y = 43$ over $1 < x < 11$ and $y < 22$ .

2005 iTest (Problems, Answer Key)
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2005 iTest Problems/Problem 16

Problem

Solution 1

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