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?
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.
To determine who got the better deal, we need to compare the cost per meal for both families.
For the Johnsons:
Cost of 2 burger meals = $46
Cost of 5 hot dog meals = $46
Total cost for 7 meals = $46 + $46 = $92
Cost per meal for the Johnsons = $92 / 7 = $13.14
For the Wilsons:
Cost of 5 burger meals = $52
Cost of 2 hot dog meals = $52
Total cost for 7 meals = $52 + $52 = $104
Cost per meal for the Wilsons = $104 / 7 = $14.86
Comparing the cost per meal, we see that the Johnsons got the better deal as they paid $13.14 per meal compared to the Wilsons who paid $14.86 per meal.
To determine who got the better deal between the Johnsons and the Wilsons, we can compare the cost per meal for each family.
Let's start by finding the cost per burger meal for each family:
- The Johnsons bought 2 burger meals for $46, so the cost per burger meal for the Johnsons is $46 divided by 2, which is $23 per burger meal.
- The Wilsons bought 5 burger meals for $52, so the cost per burger meal for the Wilsons is $52 divided by 5, which is $10.40 per burger meal.
Next, let's find the cost per hot dog meal for each family:
- The Johnsons bought 5 hot dog meals for $46, so the cost per hot dog meal for the Johnsons is $46 divided by 5, which is $9.20 per hot dog meal.
- The Wilsons bought 2 hot dog meals for $52, so the cost per hot dog meal for the Wilsons is $52 divided by 2, which is $26 per hot dog meal.
Now we can compare the costs per meal for each family:
- The Johnsons paid $23 per burger meal and $9.20 per hot dog meal.
- The Wilsons paid $10.40 per burger meal and $26 per hot dog meal.
Comparing the costs, we can see that the Wilsons got a better deal on both the burger meals and the hot dog meals. The Wilsons paid a lower cost per meal for both types of meals compared to the Johnsons.
Therefore, based on the given prices, the Wilsons got the better deal.