JAMB 2001 · UME · Q12

Find the integral values of $x$ and $y$ satisfying the inequality $3y + 5x \le 15$ , given that $y > 0$ , $y < 3$ and $x > 0$ .

Worked solution (try it first)

$y$ is a whole number with $0 < y < 3$ , so $y = 1$ or $2$ .
Also $x$ is a whole number with $x > 0$ .
Test the points in $3y + 5x$ : $(1, 1)$ gives 8, $(1, 2)$ gives 11 and $(2, 1)$ gives 13, all $\le 15$ .
Other points fail: $(2, 2)$ gives 16 and $(3, 1)$ gives 18.
So the points are $(1, 1)$ , $(1, 2)$ and $(2, 1)$ , option C.