The neighborhood skateboard club is starting a fundraiser in order to buy more skateboards. They have decided to sell logo mugs. The Mugs on Mugs Company offers to supply mugs to the club for $3.75 each plus a $55 process and handling fee. The Punny-Cups Company offers to supply mugs to the club for $5.05 each plus a $10 process and handling fee. How many mugs would they have to buy to make the cost the same from both companies? Round your answer up to the nearest one mug. Define two variables, write a system of equations, and solve the system by graphing on your own paper to find the number of mugs. Include the intersection point in your explanation.

mugs on mugs cost=3.75n+55 Punny-cups cost=5.05n+10 3.75(35)+55= 186.25-- 187. 5.05(35)+10= 186.75-- 187. intersection point= (34.04, 182.65)

mugs on mugs cost=3.75n+55
Punny-cups cost=5.05n+10

3.75(35)+55= 186.25-- 187.
5.05(35)+10= 186.75-- 187.

intersection point= (34.04, 182.65)

Heres my question:
Under what circumstances should the club choose the Mugs on Mugs Company? Under what circumstances should the club choose the Punny-Cups Company? Assume that the companies produce mugs of equal size and quality.

Check the cost from each company for 20 mugs. Do the same for 60 mugs.

If you have to pay for the mugs, what would you do in each of the cases?

To determine under what circumstances the club should choose Mugs on Mugs Company or Punny-Cups Company, we need to compare the cost per mug from each company.

Mugs on Mugs Company cost per mug: $3.75n + $55
Punny-Cups Company cost per mug: $5.05n + $10

The club should choose Mugs on Mugs Company under the following circumstances:
1. If the cost per mug from Mugs on Mugs Company is lower than the cost per mug from Punny-Cups Company for the desired number of mugs.
2. If the club wants to minimize the cost and is willing to accept the higher process and handling fee of $55.

The club should choose Punny-Cups Company under the following circumstances:
1. If the cost per mug from Punny-Cups Company is lower than the cost per mug from Mugs on Mugs Company for the desired number of mugs.
2. If the club wants to minimize the overall cost per mug and is willing to accept the lower process and handling fee of $10.

It is important to note that the decision also depends on the desired number of mugs. In the given scenario, we found that at the intersection point of (34.04, 182.65), both companies offer approximately the same cost per mug. So, for 34 mugs or fewer, the club should choose Mugs on Mugs Company, and for 35 mugs or more, the club should choose Punny-Cups Company.