Question

The number of solutions of the equation $2x + y = 40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:

• A. 7
• B. 13
• C. 14
• D. 18
• E. 20

Hint:

Translate conditions into inequalities and check integer ranges for counting solutions.

Answer 1

The Correct Option is B

From $2x + y = 40$, $y = 40 - 2x$. For $y$ positive: \[ 40 - 2x>0 \Rightarrow x<20 \] Also $x \leq y$: \[ x \leq 40 - 2x \Rightarrow 3x \leq 40 \Rightarrow x \leq 13.\overline{3} \] So $x$ is integer from 1 to 13, giving 13 solutions. \[ \boxed{13} \]