Question

Key: 0.40x+15 [pens] 1.50y+30 [sportpack]
Key continued: (0.40x+15)+(1.50y+30)≤3,330

1. If you order 500 of the first item, how many of the second item can be ordered? Show your work. (4 points: 3 points for showing work, 1 for answer.)

Answer 1

$\bf \stackrel{\textit{cost of the pens}}{0.40x+15}\qquad \qquad \qquad \stackrel{\textit{cost of the sportpacks}}{1.50y+30} \\\\\\\ \stackrel{x=500}{[0.40(500)+15]}~~+~~[1.50y+30] \le 3330 \\\\\\ 200+15~~+~~1.5y+30\le 3330\implies 245+1.5y \le 3330 \\\\\\ 1.5y\le 3085\implies y\le \cfrac{3085}{1.5}\implies y\le \cfrac{6170}{3}\implies y\le 2056\frac{2}{3}$

or namely 2056 sportpacks if we toss away the fraction.