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.
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.
To determine which meal is the best deal, we need to find the cost of each individual item. Let's solve the given system of equations step by step:
Let's assume the cost of a hot dog meal is represented by 'h' and the cost of a hamburger meal is represented by 'b'.
From the information given, we can create the following equations:
Equation 1: 5h + 2b = 46
Equation 2: 5b + 2h = 52
To solve this system of equations, we can use the method of substitution:
Step 1: Solve Equation 1 for 'h':
5h + 2b = 46
5h = 46 - 2b
h = (46 - 2b) / 5
Step 2: Substitute the value of 'h' into Equation 2:
5b + 2((46 - 2b) / 5) = 52
Simplify the equation:
5b + (92 - 4b) / 5 = 52
Multiply the entire equation by 5 to get rid of the fraction:
5(5b) + (92 - 4b) = 260
25b + 92 - 4b = 260
Combine like terms:
21b + 92 = 260
Subtract 92 from both sides:
21b = 260 - 92
21b = 168
Divide both sides by 21:
b = 168 / 21
b = 8
Step 3: Substitute the value of 'b' back into Equation 1 to find 'h':
5h + 2(8) = 46
5h + 16 = 46
5h = 46 - 16
5h = 30
Divide by 5:
h = 30 / 5
h = 6
Therefore, the cost of a hot dog meal (h) is $6 and the cost of a hamburger meal (b) is $8.
To determine the best deal, we need to compare the prices of each item.
A hot dog meal is $6, and a hamburger meal is $8.
Comparing the prices, we can conclude that the hot dog meal is the better deal, as it is cheaper than the hamburger meal.
To determine which meal is the best deal, we need to calculate the cost per meal for each option. Let's assign variables to represent the cost of a hot dog meal and a hamburger meal.
Let's say the cost of a hot dog meal is H, and the cost of a hamburger meal is B.
According to the given information, we know that:
5 hot dog meals + 2 hamburger meals = $46 ----(equation 1)
5 hamburger meals + 2 hot dog meals = $52 ----(equation 2)
We can use these two equations to solve for the cost of each meal.
Step 1: Solve for H in terms of B using equation 1.
5H + 2B = 46
5H = 46 - 2B
H = (46 - 2B) / 5 ----(equation 3)
Step 2: Substitute H from equation 3 into equation 2.
5B + 2((46 - 2B) / 5) = 52
5B + (92 - 4B) / 5 = 52
25B + 92 - 4B = 260 [Multiply through by 5 to eliminate the denominator]
21B = 260 - 92
21B = 168
B = 168 / 21
B = 8
Step 3: Substitute B = 8 into equation 3 to find the value of H.
H = (46 - 2(8)) / 5
H = (46 - 16) / 5
H = 30 / 5
H = 6
So, the cost of a hot dog meal (H) is $6, and the cost of a hamburger meal (B) is $8.
To determine the best deal, we compare the cost per meal for each option:
For the hot dog meals: $6 per meal
For the hamburger meals: $8 per meal
Since the hot dog meals are cheaper per meal, the hot dog meal is the best deal.