Stefan bought 2 turkey sandwiches and 5 ham sandwiches for a total cost of $40.50. Nancy bought 4 turkey sandwiches and 1 ham sandwich for a total cost of $31.50. The equations below represent Stefan's and Nancy's purchases.
{2t+5h=40.504t+h=31.50
What is the cost of one turkey sandwich?
To find the cost of one turkey sandwich, we need to solve the given system of equations.
Let's start by assigning variables to the unknowns. Let t represent the cost of one turkey sandwich and h represent the cost of one ham sandwich.
The system of equations can be written as:
2t + 5h = 40.50 ...(equation 1)
4t + h = 31.50 ...(equation 2)
To solve this system, we can use the method of substitution.
From equation 2, we can solve for h in terms of t:
h = 31.50 - 4t
Now substitute this value of h in equation 1:
2t + 5(31.50 - 4t) = 40.50
Simplify the equation:
2t + 157.50 - 20t = 40.50
Combine like terms:
-18t = -117
Divide both sides by -18:
t = -117 / -18
Simplify the fraction:
t ≈ 6.50
Therefore, the cost of one turkey sandwich is approximately $6.50.
2t+5h=40.50
4t+h=31.50
Multiply second equation by 5, then subtract the first equation from the second. You should be able to take it from there.