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)

Question

answer choices, how many burger meals, how many hot dog meals, the cost of a burger meal, the cost of a hot dog meal the total cost of a burger+ hot dog meal, neither, both, the jhonson's, the wilsons

Answer 1

To solve the problem, we need to set up a system of equations based on the information given:

Let:

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

From the information provided:

1. The Johnsons bought 2 burger meals and 5 hot dog meals for $46: \[ 2b + 5h = 46 \quad (1) \]
2. The Wilsons bought 5 burger meals and 2 hot dog meals for $52: \[ 5b + 2h = 52 \quad (2) \]

We can solve these equations to find \( b \) and \( h \).

From equation (1), we can express \( h \) in terms of \( b \): \[ 5h = 46 - 2b \implies h = \frac{46 - 2b}{5} \quad (3) \]

Now substitute \( h \) from equation (3) into equation (2): \[ 5b + 2\left(\frac{46 - 2b}{5}\right) = 52 \]

Multiply through by 5 to eliminate the fraction: \[ 25b + 2(46 - 2b) = 260 \] \[ 25b + 92 - 4b = 260 \] \[ 21b + 92 = 260 \] \[ 21b = 260 - 92 \] \[ 21b = 168 \] \[ b = \frac{168}{21} = 8 \]

Now substitute \( b = 8 \) back into equation (3) to find \( h \): \[ h = \frac{46 - 2(8)}{5} = \frac{46 - 16}{5} = \frac{30}{5} = 6 \]

Thus:

• Cost of a burger meal, \( b = 8 \)
• Cost of a hot dog meal, \( h = 6 \)

Now to answer the multiple-choice question based on the given solution (8, 6), we have:

• The cost of a burger meal is \( 8 \)
• The cost of a hot dog meal is \( 6 \)

Based on the choices provided, the answers would be:

• The cost of a burger meal: 8
• The cost of a hot dog meal: 6

If those are part of the choices, then both of those answers are correct. If the question asks for a specific choice such as "the cost of a burger meal" or "the cost of a hot dog meal," then you can select as appropriate. If you need further clarification or the exact choice format, please provide additional context!

Answer 2

who got the better deal

Answer 3

To determine who got the better deal between the Johnsons and the Wilsons, we can calculate the total cost per meal for both families.

For the Johnsons:

• They bought 2 burger meals and 5 hot dog meals.

• The cost breakdown is:

  • 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 ordered: \( 2 + 5 = 7 \)

• Cost per meal for the Johnsons: \[ \frac{46}{7} \approx 6.57 \]

For the Wilsons:

• They bought 5 burger meals and 2 hot dog meals.

• The cost breakdown is:

  • 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 ordered: \( 5 + 2 = 7 \)

• Cost per meal for the Wilsons: \[ \frac{52}{7} \approx 7.43 \]

Conclusion:

• Johnsons' cost per meal: approximately $6.57
• Wilsons' cost per meal: approximately $7.43

Since the Johnsons paid less per meal, the Johnsons got the better deal.