Posted by Jordan on .
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 PunnyCups 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.
Can someone tell me how to set this up?

Algebra 
MathMate,
"The Mugs on Mugs Company offers to supply mugs to the club for $3.75 each plus a $55 process and handling fee. "
Mugs(n) = 55 + 3.75n
"The PunnyCups Company offers to supply mugs to the club for $5.05 each plus a $10 process and handling fee. "
Punny(n) = ??
Can you take it from here? 
Algebra 
Jordan,
Well, does it mean that n has to be the same for both?

Algebra 
MathMate,
These are separate functions (straight lines) that you would graph. For a particular of n, you would have a value (cost) for each function, which allows you to compare prices according to the quantities of mugs to be ordered.
The crossing of the two lines is the point where the companies charge the same price.
See also previous response by Mr. Pursley.