The Johnsons and the Wilsons went to the Burger Barn for dinner.
The Johnsons bought 2 burger meals and 5 hot dog meals for $46.
The Wilsons bought 5 burger meals and 2 hot dog meals for $52.
When you solve, you get a solution of (8, 6).
What does the 8 mean in context?
In this context, the "8" represents the number of burger meals purchased by the Johnsons and the Wilsons combined.
In this context, the number 8 represents the total number of meals purchased by both the Johnsons and the Wilsons combined.
To understand what the number 8 represents in this context, we first need to analyze how we arrived at the solution of (8, 6).
Given that the Johnsons bought 2 burger meals and 5 hot dog meals for $46, and the Wilsons bought 5 burger meals and 2 hot dog meals for $52, we can set up a system of equations to represent this information.
Let's assign variables to the unknowns in our problem. Let x represent the cost of a burger meal and y represent the cost of a hot dog meal.
For the Johnsons: 2x + 5y = 46
For the Wilsons: 5x + 2y = 52
To solve this system, we have multiple methods at our disposal, such as substitution, elimination, or using matrices. However, let's focus on using the elimination method, which involves eliminating one variable by multiplying one or both equations so that the coefficients of one variable will be equal but opposite in sign.
Multiplying the first equation by 5 and the second equation by 2:
10x + 25y = 230
10x + 4y = 104
As we can see, multiplying the equations allows us to eliminate the x-term by subtraction:
(10x - 10x) + (25y - 4y) = 230 - 104
21y = 126
y = 6
Now that we've found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
2x + 5(6) = 46
2x + 30 = 46
2x = 16
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 6, or (8, 6).
Now, going back to the question of what the 8 means in context, the 8 represents the cost of a burger meal. In this scenario, it indicates that each burger meal costs $8.