Answer: $8.64 and $7.79 respectively.
Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:
3p + 2c = 41.50
2p + 5c = 43.25
The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.
By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:
First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:
15p + 10c = 207.50
6p + 15c = 129.75
Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:
15p + 10c = 207.50
6p + 15c = 129.75
9p = 207.50 - 129.75
9p = 77.75
p = 77.75 / 9
p = 8.64
Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:
3p + 2c = 41.50
3(8.64) + 2c = 41.50
25.92 + 2c = 41.50
2c = 41.50 - 25.92
2c = 15.58
c = 15.58 / 2
c = 7.79
Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.