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).(3 points) What does the 8 mean in context?What does the 6 mean in context?Who got the better deal?

Answer 1

To solve the problem, we need to define the variables based on the context of the meals purchased.

Let's define:

• \( b \) as the price of a burger meal
• \( h \) as the price of a hot dog meal

From the information given, we can set up the following equations based on the purchases made by the Johnsons and the Wilsons:

1. For the Johnsons: \[ 2b + 5h = 46 \]

2. For the Wilsons: \[ 5b + 2h = 52 \]

The solution (8, 6) indicates:

• The value \( b = 8 \): This means that the price of a burger meal is $8.
• The value \( h = 6 \): This means that the price of a hot dog meal is $6.

Now, to determine who got the better deal, we can calculate the total cost for both families based on their orders:

Johnsons:

• 2 burger meals: \( 2 \times 8 = 16 \)
• 5 hot dog meals: \( 5 \times 6 = 30 \)
• Total cost for the Johnsons: \( 16 + 30 = 46 \)

Wilsons:

• 5 burger meals: \( 5 \times 8 = 40 \)
• 2 hot dog meals: \( 2 \times 6 = 12 \)
• Total cost for the Wilsons: \( 40 + 12 = 52 \)

Better deal: To assess who got the better deal, we can look at the total quantity of meals purchased divided by the total cost:

• The Johnsons bought 2 burger meals and 5 hot dog meals, totaling 7 meals. Their cost was $46. \[ \text{Cost per meal for the Johnsons} = \frac{46}{7} \approx 6.57 \]

• The Wilsons bought 5 burger meals and 2 hot dog meals, totaling 7 meals. Their cost was $52. \[ \text{Cost per meal for the Wilsons} = \frac{52}{7} \approx 7.43 \]

Conclusion: The Johnsons got the better deal because they paid approximately $6.57 per meal, while the Wilsons paid approximately $7.43 per meal.

Answer 2

What does the 8 mean in context?

Answer 3

In context, the value \( 8 \) refers to the price of a burger meal at the Burger Barn. Specifically, it means that each burger meal costs $8. This information helps us understand the pricing structure for the meals ordered by both the Johnsons and the Wilsons.

Answer 4

What does the 6 mean in context?

Answer 5

In context, the value \( 6 \) refers to the price of a hot dog meal at the Burger Barn. Specifically, it means that each hot dog meal costs $6. This pricing information is important for understanding the total costs incurred by both the Johnsons and the Wilsons for their respective meal orders.

Answer 6

Who got the better deal?

Answer 7

To determine who got the better deal, we can calculate the cost per meal for both families based on the meals they purchased.

Johnsons:

• Meals Ordered: 2 burger meals and 5 hot dog meals
• Cost Calculation:
  • Cost of burger meals: \( 2 \times 8 = 16 \)
  • Cost of hot dog meals: \( 5 \times 6 = 30 \)
  • Total cost for the Johnsons: \( 16 + 30 = 46 \)
• Total Meals: 2 + 5 = 7 meals

Cost per meal for the Johnsons: \[ \text{Cost per meal} = \frac{\text{Total cost}}{\text{Total meals}} = \frac{46}{7} \approx 6.57 \]

Wilsons:

• Meals Ordered: 5 burger meals and 2 hot dog meals
• Cost Calculation:
  • Cost of burger meals: \( 5 \times 8 = 40 \)
  • Cost of hot dog meals: \( 2 \times 6 = 12 \)
  • Total cost for the Wilsons: \( 40 + 12 = 52 \)
• Total Meals: 5 + 2 = 7 meals

Cost per meal for the Wilsons: \[ \text{Cost per meal} = \frac{\text{Total cost}}{\text{Total meals}} = \frac{52}{7} \approx 7.43 \]

Conclusion:

• Johnsons: Approximately $6.57 per meal
• Wilsons: Approximately $7.43 per meal

The Johnsons got the better deal because they paid approximately $6.57 per meal, while the Wilsons paid approximately $7.43 per meal.