To interpret the solution (8, 6) in the context of the given problem, we need to define what the variables represent.
Let's assume:
- \( x \) represents the cost of a burger meal,
- \( y \) represents the cost of a hot dog meal.
Given the equations:
- For the Johnsons: \( 2x + 5y = 46 \)
- For the Wilsons: \( 5x + 2y = 52 \)
After solving the equations, we get the solution \( (8, 6) \):
- The 8 represents the cost of a burger meal. So, each burger meal costs $8.
- The 6 represents the cost of a hot dog meal. So, each hot dog meal costs $6.
Now, to determine who got the better deal, we need to analyze the total costs for both families:
Johnsons:
- They bought 2 burger meals and 5 hot dog meals.
- Total cost: \( 2(8) + 5(6) = 16 + 30 = 46 \) (which fits the given information).
Wilsons:
- They bought 5 burger meals and 2 hot dog meals.
- Total cost: \( 5(8) + 2(6) = 40 + 12 = 52 \) (which also fits the given information).
Now, let's figure out how much each family spent per meal:
-
Total meals for Johnsons = 2 + 5 = 7 meals.
- Cost per meal for Johnsons: \[ \frac{46}{7} \approx 6.57 \text{ per meal} \]
-
Total meals for Wilsons = 5 + 2 = 7 meals.
- Cost per meal for Wilsons: \[ \frac{52}{7} \approx 7.43 \text{ per meal} \]
Comparing the average cost per meal:
- Johnsons: approximately $6.57 per meal
- Wilsons: approximately $7.43 per meal
Since the average cost per meal is lower for the Johnsons, we can conclude that the Johnsons got the better deal.
Final Answer:
- The 8 means the cost of a burger meal ($8).
- The 6 means the cost of a hot dog meal ($6).
- The Johnsons got the better deal.