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 need to find the cost of each burger meal and each hot dog meal based on the information provided, and then calculate the cost per meal for both the Johnsons and the Wilsons.

We can set up two equations based on the information given:

1. For the Johnsons:
\[ 2B + 5H = 46 \]

2. For the Wilsons:
\[ 5B + 2H = 52 \]

Where \( B \) is the price of a burger meal and \( H \) is the price of a hot dog meal.

We have the solution (8, 6) which indicates:
- \( B = 8 \) (each burger meal costs $8)
- \( H = 6 \) (each hot dog meal costs $6)

Now, we can calculate the total cost for each family:

### Johnsons:
- They bought 2 burger meals and 5 hot dog meals:
\[
\text{Total cost} = (2 \times 8) + (5 \times 6) = 16 + 30 = 46
\]

### Wilsons:
- They bought 5 burger meals and 2 hot dog meals:
\[
\text{Total cost} = (5 \times 8) + (2 \times 6) = 40 + 12 = 52
\]

Now we can compare the cost per meal for each family.

### Johnsons:
- Total meals = 2 (burgers) + 5 (hot dogs) = 7 meals
- Cost per meal = \( \frac{46}{7} \approx 6.57 \)

### Wilsons:
- Total meals = 5 (burgers) + 2 (hot dogs) = 7 meals
- Cost per meal = \( \frac{52}{7} \approx 7.43 \)

### Conclusion:
- Johnsons: \( \approx 6.57 \) per meal
- Wilsons: \( \approx 7.43 \) per meal

**The Johnsons got the better deal** as they paid approximately $6.57 per meal compared to the Wilsons who paid approximately $7.43 per meal.