Question

41. The Puuur Place builds customized cat trees for pet owners. The basic tree is$100 and each additional platform, perch, or toy costs $50. Meow Now alsobuilds customized cat trees. Their basic cat tree starts at $50 and eachadditional piece costs $75.[A] Write and solve a system of equations to represent the total cost, y, when xadditional pieces are purchased with a basic cat tree at each store.[B] Solve this system of equations and show your work.[C] Graph the system of equations.[D] Reggie wants to purchase a cat tree for his pets. Use your graph to explainwhich store would be cheaper depending on how many add-ons he wants topurchase.HELLLLP

Answer 1

In this problem, we need to apply systems of equations to buying Cat Trees.

We are given to companies with different conditions, so we can write these equations.

Part [A]

One company, PP, offers the following deal:

- $100 for the cat tree,

- and $50 for each additional part or toy.

The second company, MN, offers this deal:

- $50 for a basic cat tree

- $75 for each additional part

For both companies, let x represent the additional pieces and y represent the total cost. Then we get

`\begin{gathered} \text{ PP}:y=50x+100 \\ \\ \text{ MN}:y=75x+50 \end{gathered}`

Part [C]

One way to solve this system is by graphing the equations. We can do this by creating a simple table for each function, then graph the points. Which numbers this large, a table is the better way to go.

Let's begin with the company PP:

`y=50x+100`

A simple table gives us

Graphing those points, we have:

Next, we move on to the company MN:

`y=75x+50`

We can create a similar table and graph it on the same coordinate plane.

Part [D]

Finally, we want to talk about someone trying to decide the best place to purchase the cat tree depending on how many add-on's he want to buy.

Based on the graph, we see that the cat trees will cost the same if he buys 2 add-ons.

If he chooses to buy less than 2 add-ons, the MN company wil give the cheaper prices (in blue).

If he wants to buy more than 2 add-ons, the PP company will get him the cheaper overall cost.