To solve the problem, we can start by defining the variables based on the given context:
- Let \( b \) represent the price of one burger meal.
- Let \( h \) represent the price of one hot dog meal.
From the information given, we can set up the following equations based on the purchases:
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For the Johnsons:
\( 2b + 5h = 46 \) (Equation 1) -
For the Wilsons:
\( 5b + 2h = 52 \) (Equation 2)
To make sense of the solution mentioned, \( (8, 6) \), we need to identify what these numbers represent. Specifically, they represent the values of \( b \) and \( h \).
- In this context, the solution means:
- 8 is the price of one burger meal (i.e., \( b = 8 \)).
- 6 is the price of one hot dog meal (i.e., \( h = 6 \)).
Now, let's determine who got the better deal:
-
Johnsons' Total Cost:
- For 2 burger meals and 5 hot dog meals: \[ \text{Total} = 2(8) + 5(6) = 16 + 30 = 46 \] This confirms their total cost matches the given information.
-
Wilsons' Total Cost:
- For 5 burger meals and 2 hot dog meals: \[ \text{Total} = 5(8) + 2(6) = 40 + 12 = 52 \] This confirms their total cost matches the given information.
To find out who got the better deal, we can calculate the cost per meal for both families:
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Johnsons:
- Total meals = 2 burgers + 5 hot dogs = 7 meals.
- Cost per meal = \( \frac{46}{7} \approx 6.57 \).
-
Wilsons:
- Total meals = 5 burgers + 2 hot dogs = 7 meals.
- Cost per meal = \( \frac{52}{7} \approx 7.43 \).
Conclusion: The Johnsons got the better deal since they paid approximately $6.57 per meal, compared to the Wilsons who paid approximately $7.43 per meal.
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