Question

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.




First, select the point on the graph that represents Sean's break-even point, which is the point where the costs to make the games will equal the revenue from selling them. Notice that the revenue equation has already been graphed.


Then, determine the least number of games Sean will need to sell in order to make a profit. Profit occurs when revenue is greater than the cost.

Answer 1

So the first task is to:
First, select the point on the graph that represents Sean's break-even point, which is the point where the costs to make the games will equal the revenue from selling them. Notice that the revenue equation has already been graphed.

We know the initial cost of $300 for supplies, $50 per each game and it's going to be sold at $85.

The graph shows four points. The first one being at 5 games sold, with approximately $425 collected. The second one at around 8.5 games sold, which is about $725. The third one is ten games sold, with $850 collected. The last one is around 11.8 game sold, with approximately $1000 gained.

So: 50 x 5 + 300 = 550 (Cost per game + initial cost)

85 x 5 = 425 (Cost of games sold) That removes the first point.

50 x 8.5 + 300 = 725

85 x 8.5 = 722 (Close enough:)

That gave us it took Sean 8.5 games to have a revenue equal to the cost of making them.

Then, the second task is to:

Determine the least number of games Sean will need to sell in order to make a profit. Profit occurs when revenue is greater than the cost.

The choices are at 5, 8, 9, or 10 games.

Since we previously found out that it took him 8.5 games to have an equal revenue to the cost, we can easily knot that it took him 9 games to make a profit.

But just for sure:
50 x 9 + 300 = 750

85 x 9 = 765

Peace:D

ヾ(•ω•`)o