Hot dogs and Hamburgers: The caterer for your class picnic charges $1 for each hotdog and $2 for each hamburger. You have $48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could purchase.

$1(#hd) + $2(#ham) = $48

Thanks DrBob222 :D

To write a model that shows the different numbers of hot dogs and hamburgers you could purchase, we can start by defining variables. Let's use "x" to represent the number of hot dogs and "y" to represent the number of hamburgers.

Given that each hot dog costs $1 and each hamburger costs $2, we can set up the following equations to represent the cost:

Cost of hot dogs: 1 * x = 1x
Cost of hamburgers: 2 * y = 2y

Since you have $48 to spend, we can also set up the following equation to represent the total cost:

Total cost: 1x + 2y = 48

Now, let's express the variables x and y in terms of each other to find the different combinations:

From the Total cost equation, we can rewrite it as:
1x = 48 - 2y

This equation shows that the number of hot dogs is equal to 48 minus two times the number of hamburgers.

Now, we can substitute this expression for x into the Cost of hot dogs equation:
1(48 - 2y)

Simplifying:
48 - 2y

This equation represents the different numbers of hot dogs (x) and hamburgers (y) that you could purchase with $48.

To find the possible combinations, you can plug in integer values for y, starting from 0, and calculate the corresponding values for x. For example:

If y = 0, then x = 48 - 2(0) = 48
If y = 1, then x = 48 - 2(1) = 46
If y = 2, then x = 48 - 2(2) = 44

Continue this process for different values of y until you find all possible combinations.