Question

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).
Who got the better deal?

Answer 1

To determine who got the better deal, we can calculate the cost per meal for each family.

For the Johnsons:
Cost of 2 burger meals = 2x (x is the cost of a burger meal)
Cost of 5 hot dog meals = 5y (y is the cost of a hot dog meal)
Total cost for the Johnsons = 2x + 5y = $46

For the Wilsons:
Cost of 5 burger meals = 5x
Cost of 2 hot dog meals = 2y
Total cost for the Wilsons = 5x + 2y = $52

From the given solution (8, 6), we can substitute these values for x and y to check if they satisfy the given equations.
For x = 8 and y = 6:
2(8) + 5(6) = 16 + 30 = 46 --> satisfies the Johnsons' equation
5(8) + 2(6) = 40 + 12 = 52 --> satisfies the Wilsons' equation

Therefore, both families got the same deal with a cost per meal of $8 for burgers and $6 for hot dogs.