Two groups of people order food at a restaurant. One group orders
4 hamburgers and 7 chicken sandwiches for $34.50. The other group orders 8 hamburgers and 3 chicken sandwiches for $30.50. Find the cost of each item.
add up the costs:
4h+7c = 34.50
8h+3c = 30.50
Now just solve the system for h and c.
To find the cost of each item, we can use a system of equations. Let's assign variables to the unknowns:
Let's say the cost of a hamburger is 'x' dollars, and the cost of a chicken sandwich is 'y' dollars.
From the information given, we can form two equations:
Equation 1: 4x + 7y = 34.50
Equation 2: 8x + 3y = 30.50
Now we can solve this system of equations to find the values of 'x' and 'y'.
One way to solve this system is by using the method of substitution. We can solve Equation 1 for 'x' and substitute it into Equation 2, or vice versa. Let's solve Equation 1 for 'x':
4x + 7y = 34.50
4x = 34.50 - 7y
x = (34.50 - 7y)/4
Now we substitute this expression for 'x' into Equation 2:
8x + 3y = 30.50
8((34.50 - 7y)/4) + 3y = 30.50
Let's simplify this equation:
69 - 14y + 3y = 30.50
-11y = -38.50
y = 3.50
Now we substitute the value of 'y' back into Equation 1 to find the value of 'x':
4x + 7(3.50) = 34.50
4x + 24.50 = 34.50
4x = 10
x = 2.50
Therefore, the cost of each hamburger is $2.50, and the cost of each chicken sandwich is $3.50.