Question

The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?

Answer 1

$\displaystyle \textsf{The problem implies that each hot}\\ \textsf{dog costs}\,\, \$2.\\ \textsf{Also, it implies}\,\, x \,\, \textsf{represents the}\\ \textsf{amount of hot dogs sold}.\\ \textsf{So},\,\,2\,\, \textsf{is to be multiplied by}\\ x . \\ \textsf{The first statement of the problem implies that}\\ \textsf{the owner has to pay}\,\, \$48 \,\, \textsf{every morning}\\ \textsf{morning for supplies. So the owner loses}\,\, \$48 \\ \textsf{everyday} \\ \therefore \textsf{The equation is}\,\, y = 2x - 48$