Tony is in charge of the concession stand. He charges four dollars for two hotdogs and two sodas. He charges for 50 for three hotdogs and one soda. How much is there a charge for hotdog how much for soda
Let's assume the cost of a hotdog is x dollars and the cost of a soda is y dollars.
From the information given, we can create two equations:
2x + 2y = 4 (equation 1)
3x + y = 5 (equation 2)
Simplifying equation 1 by dividing both sides by 2, we get:
x + y = 2 (equation 3)
Subtract equation 3 from equation 2 to eliminate the y variable:
3x + y - (x + y) = 5 - 2
2x = 3
x = 3/2
x = 1.5
Now, we can substitute the value of x into equation 3 to find the cost of a soda:
1.5 + y = 2
y = 2 - 1.5
y = 0.5
Therefore, Tony charges $1.5 for a hotdog and $0.5 for a soda.
To determine the cost of a hotdog and a soda separately, let's solve the given equations simultaneously:
Let's denote the cost of a hotdog as "H" and the cost of a soda as "S."
From the first scenario:
2H + 2S = $4 --- Equation 1
From the second scenario:
3H + S = $5 --- Equation 2
To solve the equations, we can use the method of substitution:
Rearrange Equation 2 to solve for S:
S = $5 - 3H
Substitute this value of S into Equation 1:
2H + 2($5 - 3H) = $4
Distribute 2 to the terms inside the parentheses:
2H + $10 - 6H = $4
Combine like terms:
-4H + $10 = $4
Subtract $10 from both sides of the equation:
-4H = $4 - $10
Simplify:
-4H = -$6
Divide both sides of the equation by -4:
H = $6 / 4
H = $1.50
Now, substitute the value of H back into Equation 2 to find S:
3($1.50) + S = $5
Multiply:
$4.50 + S = $5
Subtract $4.50 from both sides of the equation:
S = $5 - $4.50
Simplify:
S = $0.50
So, the charge for a hotdog is $1.50, and the charge for a soda is $0.50.