The Woodson and Baker families went to the Burger Shack for dinner. The Woodsons bought 3 burger meals and 4 hot dog meals for $48. The Bakers bought 6 burger meals and 2 hot dog meals for $60. How much does each meal cost? Show your work.
Let's use the variables b for the cost of a burger meal and h for the cost of a hot dog meal.
From the information given, we can create a system of equations:
3b + 4h = 48 (for the Woodsons)
6b + 2h = 60 (for the Bakers)
To solve for b and h, we can use the method of substitution.
From the first equation, we can solve for h:
4h = 48 - 3b
h = (48 - 3b)/4
Now we can substitute this expression for h into the second equation:
6b + 2((48 - 3b)/4) = 60
6b + 24 - 6b = 60
24 = 60
This equation has no solution, which means there must have been a mistake in the information provided.
If x represents the cost of burger meals, then y represents
If x represents the cost of burger meals, then y represents the cost of hot dog meals.
The system of linear equations would look like
The system of linear equations would look like:
3x + 4y = 48
6x + 2y = 60
How much does a burger meal cost?
To find the cost of a burger meal, we can solve the system of equations:
3x + 4y = 48
6x + 2y = 60
Let's solve this system using the substitution method.
From the first equation:
3x = 48 - 4y
x = (48 - 4y)/3
Now substitute this expression for x into the second equation:
6((48 - 4y)/3) + 2y = 60
2(48 - 4y) + 2y = 60
96 - 8y + 2y = 60
-6y = -36
y = 6
Now substitute y = 6 back into the expression for x:
x = (48 - 4(6))/3
x = (48 - 24)/3
x = 24/3
x = 8
Therefore, a burger meal costs $8.