Final answer:
Hank purchased 7 bacon cheeseburgers and 3 meat-stuffed baked potatoes. A system of equations was created based on the total cost and number of items purchased, and it was solved to find the quantities of each item.
Step-by-step explanation:
To determine how many bacon cheeseburgers and meat-stuffed baked potatoes Hank purchased, we need to set up a system of equations to find the number of each item. Let's denote B as the number of bacon cheeseburgers and P as the number of meat-stuffed baked potatoes.
From the information given, we can express the total cost of these items as:
8.99B + 7.49P = 85.40
Since we know Hank purchased a total of 10 burgers and potatoes, we can also write:
B + P = 10
Now we have two equations:
- 8.99B + 7.49P = 85.40
- B + P = 10
From the second equation, we can find P in terms of B:
P = 10 - B
Substitute P in the first equation:
8.99B + 7.49(10 - B) = 85.40
Simplify and solve for B:
8.99B + 74.90 - 7.49B = 85.40
1.50B = 10.50
B = 7
Now, substitute B back into the equation for P:
P = 10 - B
P = 10 - 7
P = 3
Hank purchased 7 bacon cheeseburgers and 3 meat-stuffed baked potatoes.