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 please! :)
momcost=3.75n+55
Puncost=5.05n+10
Well, for many cups, puncost has to be greater. Where is it the same.
Graph the two costs, vs n.
Where the lines cross, is the same.
Sure! To set up this problem, let's define two variables:
Let's call the number of mugs purchased from The Mugs on Mugs Company as "x".
Let's call the number of mugs purchased from The Punny-Cups Company as "y".
Now, let's write a system of equations based on the given information:
Equation 1: Cost from The Mugs on Mugs Company
The cost per mug from The Mugs on Mugs Company is $3.75, and there is a $55 process and handling fee. So the total cost from this company can be expressed as:
Total cost from The Mugs on Mugs Company = (3.75 * x) + 55
Equation 2: Cost from The Punny-Cups Company
The cost per mug from The Punny-Cups Company is $5.05, and there is a $10 process and handling fee. So the total cost from this company can be expressed as:
Total cost from The Punny-Cups Company = (5.05 * y) + 10
The goal is to find the number of mugs where the cost is the same from both companies. So we can set up the equation:
(3.75 * x) + 55 = (5.05 * y) + 10
To solve this system of equations by graphing, you would plot the graphs of the two equations on the same coordinate plane. The point where the graphs intersect represents the solution to the system of equations, which will give us the number of mugs needed to make the cost the same from both companies.
Please note that I am unable to graph the equations directly here, as I am a text-based AI. However, you can graph them on your own paper or using any graphing tool or software and find the intersection point of the two lines.