A party planner can spend a maximum of $5000 on food. If the chicken dinner (x) costs $20 and the steak dinner (y) costs $25, make a graph of the region that shows the possibilities for the number of chicken and steak dinners that can be purchased while still staying within budget.
join 200 on y axis to 250 on x axis.
The triangle will be your region.
To make a graph that depicts the possibilities for the number of chicken and steak dinners within the budget of $5000, we can use the information provided. Let's assign the number of chicken dinners as 'x' and the number of steak dinners as 'y'.
We know that the cost of each chicken dinner is $20 and the cost of each steak dinner is $25. Therefore, the total cost of chicken dinners can be represented as 20x and the total cost of steak dinners can be represented as 25y.
The total cost of the dinners cannot exceed $5000, so we can write the following inequality:
20x + 25y ≤ 5000
Now, let's rearrange this equation to solve for y:
25y ≤ 5000 - 20x
y ≤ (5000 - 20x) / 25
To graph this inequality, we can start by setting up a coordinate plane. Choose a suitable range for the number of chicken dinners (x) and steak dinners (y), and then plot the graph.
For example, let's assume the range for x to be 0-250 (inclusive) and for y to be 0-200 (inclusive). This gives us a wide range to see various possibilities.
Plotting the graph can be done manually or by using graphing software. The graph will show a shaded region that represents the possibilities for the number of chicken and steak dinners that can be purchased while remaining within budget.
(Note: Keep in mind that the values on the graph will be discrete since we cannot purchase fractional dinners, hence the chicken and steak numbers should be whole numbers.)
By analyzing the graph, you will be able to identify the number of chicken and steak dinners that satisfy the budget constraint.