Question

Five hot dog meals and two hamburger meals are $46 and then five hamburger meals and two hot down meals are $52. Which one is the best deal.

Answer 1

To solve this problem, we can set up a system of equations.

Let's represent the cost of a hot dog meal as h and the cost of a hamburger meal as b.

From the given information, we have the following system of equations:

5h + 2b = 46 (Equation 1)
5b + 2h = 52 (Equation 2)

To determine which deal is the best, we need to find the value of either h or b.

Let's solve this system of equations by using the elimination method:

Multiply Equation 1 by 5 and Equation 2 by 2 to have the same coefficient for 'h':

25h + 10b = 230 (Equation 3)
10b + 4h = 104 (Equation 4)

Subtract Equation 4 from Equation 3:

25h + 10b - (10b + 4h) = 230 - 104
25h + 10b - 10b - 4h = 126
21h = 126

Divide both sides of the equation by 21:

h = 126 / 21
h = 6

Now that we know the cost of a hot dog meal is $6, we can substitute this value into either Equation 1 or Equation 2 to find the cost of a hamburger meal. Let's substitute it into Equation 1:

5(6) + 2b = 46
30 + 2b = 46
2b = 46 - 30
2b = 16
b = 16 / 2
b = 8

The cost of a hamburger meal is $8.

Comparing the two prices, we can see that the hot dog meal costs $6 and the hamburger meal costs $8.

Therefore, the best deal is the hot dog meal because it is $2 cheaper than the hamburger meal.