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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?
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1 answer

To solve the problem, let’s first identify what the variables represent in the context of the scenario.

Let:

  • \( b \) = the cost of a burger meal
  • \( h \) = the cost of a hot dog meal

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

  1. From the Johnsons:
    \( 2b + 5h = 46 \)

  2. From the Wilsons:
    \( 5b + 2h = 52 \)

Now, according to your results, \( (b, h) = (8, 6) \). Thus:

  • \( b = 8 \) (the cost of a burger meal)
  • \( h = 6 \) (the cost of a hot dog meal)

Now we can answer your questions based on this context.

  1. What does 8 mean in context?

    • The 8 represents the cost of one burger meal at the Burger Barn.

  2. What does 6 mean in context?

    • The 6 represents the cost of one hot dog meal at the Burger Barn.

  3. Who got the better deal?

    • To determine who got the better deal, we can calculate the total cost of the meals for each family based on the found prices.

    Johnsons:

    • 2 burger meals: \( 2 \times 8 = 16 \)
    • 5 hot dog meals: \( 5 \times 6 = 30 \)
    • Total cost: \( 16 + 30 = 46 \) (this matches the given information)

    Wilsons:

    • 5 burger meals: \( 5 \times 8 = 40 \)
    • 2 hot dog meals: \( 2 \times 6 = 12 \)
    • Total cost: \( 40 + 12 = 52 \) (this also matches the given information)

    To compare the cost per meal:

    • Johnsons: \( \frac{46}{7} \approx 6.57 \) per meal
    • Wilsons: \( \frac{52}{7} \approx 7.43 \) per meal

    Therefore, the Johnsons got the better deal since their cost per meal is lower.