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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)
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What does the 8 mean in context?
What does the 6 mean in context?
Who got the better deal?

1 answer

First, let's define the variables used in the problem:

  • Let \( b \) represent the cost of one burger meal.
  • Let \( h \) represent the cost of one hot dog meal.

From the information provided, we have the following equations based on the purchases of the Johnsons and the Wilsons:

  1. \( 2b + 5h = 46 \) (Johnsons)
  2. \( 5b + 2h = 52 \) (Wilsons)

When you solve these equations, you get the solution \( (b, h) = (8, 6) \).

Now, let's interpret the values of \( 8 \) and \( 6 \):

  1. What does the 8 mean in context?

    • The 8 means that the cost of one burger meal is $8.

  2. What does the 6 mean in context?

    • The 6 means that the cost of one hot dog meal is $6.

  3. Who got the better deal?

    • To determine who got the better deal, we need to calculate the total cost of meals for both families based on the prices derived.

    • Johnsons:

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

    • Wilsons:

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

    Now let's calculate the cost per meal for both families:

    • Johnsons:

      • Total meals = \( 2 + 5 = 7 \)
      • Cost per meal = \( \frac{46}{7} \approx 6.57 \)

    • Wilsons:

      • Total meals = \( 5 + 2 = 7 \)
      • Cost per meal = \( \frac{52}{7} \approx 7.43 \)

Conclusion: The Johnsons got the better deal because their cost per meal is approximately $6.57, compared to the Wilsons' cost per meal of approximately $7.43.