the Johnson's and the Wilson's went to the burger barn for dinner.
the Johnson's bought 2 burger meals and 5 hot dog meals for $46
the Wilson bought 5 burger meals and 2 hot dog meals for $52
when you solve you get (8,6)
what does the 8 and 6 mean in context?
In the given context, the "8" and "6" do not have a specific meaning. It is unclear where those numbers come from and how they relate to the rest of the information provided. It seems like there might be a mistake in the given solution.
In this context of solving the system of equations, the "8" and "6" represent the number of burger meals and hot dog meals, respectively, that satisfy the conditions given in the problem.
The "8" represents the number of burger meals that the Johnson's and the Wilson's bought collectively, and the "6" represents the number of hot dog meals that they bought collectively. This solution indicates that, in total, there were 8 burger meals purchased and 6 hot dog meals purchased between the two families.
In order to understand the significance of the numbers 8 and 6 in this context, we need to decipher what the numbers represent.
From the given information, we know that the Johnsons bought 2 burger meals and 5 hot dog meals for $46, while the Wilsons bought 5 burger meals and 2 hot dog meals for $52.
To solve this problem, we can assign variables to the unknowns:
Let's say the cost of a burger meal for the Johnsons is x, and the cost of a hot dog meal is y. Similarly, let the cost of a burger meal for the Wilsons be a, and the cost of a hot dog meal be b.
With this information, we can set up two equations:
Equation 1: 2x + 5y = 46 (representing the Johnsons' order)
Equation 2: 5a + 2b = 52 (representing the Wilsons' order)
To solve these equations, we can use a method called substitution. Let's rearrange Equation 1 to solve for x:
2x = 46 - 5y
x = (46 - 5y)/2
Now substitute this value of x into Equation 2:
5((46 - 5y)/2) + 2b = 52
Simplifying this equation, we get:
23 - 2.5y + 2b = 52
To further simplify the equation, let's multiply each term by 2 to eliminate the fraction:
46 - 5y + 4b = 104
Rearranging the equation, we get:
-5y + 4b = 58
Now, we have a system of equations in terms of y and b:
-5y + 4b = 58 (Equation 3)
5a + 2b = 52 (Equation 2)
To solve this system, we can use the method of substitution or elimination.
When solving the system of equations, we find that the solution is y = 8 and b = 6.
To put these values in context, y = 8 represents the cost of a hot dog meal for both the Johnsons and the Wilsons, while b = 6 represents the cost of a burger meal for both families.
Therefore, in this context, the numbers 8 and 6 represent the cost of a hot dog meal and a burger meal, respectively, for both the Johnsons and the Wilsons.