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

What does the 8 mean in context?

Answer 2

What does the 6 mean in context?

Answer 3

Who got the better deal?

Answer 4

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 5

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 6

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 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.