Sean decides to start a small business creating and selling outdoor yard games. It will cost Sean $50 to make each game as well as an initial cost

of $300 to purchase the needed equipment and supplies. He plans to sell each game for $85,

The system of equations below models the cost and revenue for Sean's outdoor yard games where x represents the number of games and y

represents the amount, in dollars.

y = 50x + 300

y = 85

The initial cost is $300 (this cost is paid only one time) and he also must pay $50 per game, and he plans to sell each game per $85

if x is the number of games that he makes/sells and y represents the number of dollars, then we have two equations, one for the money he loses, and other for the money he wins.

y1 = - $300 - $50*x

is the equation for the money lo

y2 = $85*x

if we took the addition of those two equations, we will get te profit equation:

p (x) = $85*x - $300 - $50*x = ($85 - $50) * x - $300 = $35*x - $300

And from this equation we can find the number of games, x, that he needs to sell in order to break even:

p (x) = 0 = $35*x - $300

x = $300/$35 = 8.6

we can not have a 0.6 of a game, so we must round up to 9.

This means that he must sell at least 9 games if he does not want to lose money, after the ninth game, each sell gives a positive profit.