Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.
The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:
2x + 8y
The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:
4a + 4b
We want to find values of x, y, a, and b such that:
2x + 8y = 4a + 4b
Simplifying the equation, we get:
x + 4y = 2a + b
We also know that the total amount set aside for the purchases is $96. Therefore, we have:
2x + 8y + 4a + 4b = 96
Simplifying the equation, we get:
x + 4y + 2a + b = 48
Now, we can plot the graph of the equation:
x + 4y = 2a + b
To plot the graph, we can rearrange the equation as follows:
4y - b = 2a - x
y = (2a - x + b)/4
We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:
y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2
Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.
Here is the graph:
Graph
To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:
x + 4y + 2a + b = 48
We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.
Explanation: