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?
:: How many burger meals
:: The cost of a burger meal
:: The total cost of a burger + hot dog meal
:: How many hot dog meals
:: The cost of a hot dog meal
:: Neither
:: both
:: The Johnson's
:: The Wilsons

Answer 1

Both of these tables represent linear graphs:
*

-3
8
-2
10
-1
12

14
1
16
2
18
3
20
4
22

У
-3
-2

0

2

4



8
3
10
4
12
Does the line through the first set of points intersect with the line through the second set of points?
(1 point)
• Yes...these lines are not parallel nor perpendicular
• No...these lines are parallel
• Yes... these lines are parallel
• You cannot tell without a graph
• No... these lines are perpendicular
• Yes... these lines are perpendicular

Answer 2

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:
1. For the Johnsons: \( 2x + 5y = 46 \)
2. 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.

Answer 3

To determine whether the lines represented by the two sets of points intersect, we need to first understand the slopes of the lines and their equations.

1. **First Set of Points:**
- Points: (-3, 8), (-2, 10), (-1, 12)
- Slope Calculation:
- Using the points (-2, 10) and (-1, 12):
\[
\text{slope} = \frac{12 - 10}{-1 - (-2)} = \frac{2}{1} = 2
\]

- The slope of the first line is **2**.

2. **Second Set of Points:**
- Points: (-3, -2), (0, 2), (3, 10), (4, 12)
- Slope Calculation:
- Using the points (0, 2) and (3, 10):
\[
\text{slope} = \frac{10 - 2}{3 - 0} = \frac{8}{3}
\]

- The slope of the second line is **\(\frac{8}{3}\)** (or approximately 2.67).

### Conclusion:
- The slopes of the two lines are different (2 and \(\frac{8}{3}\)).
- Since the slopes are not equal, the lines are not parallel.
- Additionally, they are not perpendicular, because the product of their slopes is not -1 (the product of 2 and \(\frac{8}{3}\) is \(\frac{16}{3}\), which is not -1).

### Final Answer:
• Yes...these lines are not parallel nor perpendicular.