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.
Can someone tell me how to set this up?
"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 Punny-Cups 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?
Well, does it mean that n has to be the same for both?
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.
To set up this problem, we need to define two variables and create a system of equations. Let's say "x" represents the number of mugs purchased from the Mugs on Mugs Company, and "y" represents the number of mugs purchased from the Punny-Cups Company.
Let's set up the equation for the cost of purchasing from Mugs on Mugs Company. The cost per mug is $3.75, and there is a $55 process and handling fee. So the total cost from Mugs on Mugs Company would be:
Total Cost from Mugs on Mugs Company = $3.75x + $55
Now, let's set up the equation for the cost of purchasing from Punny-Cups Company. The cost per mug is $5.05, and there is a $10 process and handling fee. So the total cost from Punny-Cups Company would be:
Total Cost from Punny-Cups Company = $5.05y + $10
To find the number of mugs they would have to buy to make the costs the same from both companies, we need to find the values of "x" and "y" where the total costs are equal.
Now, you can graph the two equations on your own paper and find the intersection point. The coordinates of the intersection point will give you the values of "x" and "y," which represent the number of mugs they need to buy to make the costs the same. Round your answer up to the nearest one mug.
Once you have the intersection point, you can convert the coordinates to whole numbers as needed.