Set up an equation for each customer:
4C + 5S = 22.50
7C + 6S = 35.25
Multipyy the first equation by -1.75 to make the 4C the inverse of 7c:
4C + 5S = 22.50 x -1.75 = -7C - 8.75S = -39.375
Now add the two equations to eliminate the C variable:
7C +6S = 35.25 + -7C - 8.75S = -39.375
= -2.75S = -4.125
Divide both sides by -2.75 to solve for S:
S = -4.125 / -2.75
S = 1.50
The price of a soda is $1.50
Now replace S in an equation with 1.50 and solve for C:
4C + 5(1.50) = 22.50
Simplify:
4C + 7.50 = 22.50
Subtract 7.50 from both sides:
4C = 15
Divide both sides by 4:
C = 15/4
C = 3.75
The sandwich costs $3.75
Soda = $1.50
Sandwich = $3.75
Answer: the cost of a chicken sandwich is $3.75
the cost of a large soda is $1.5
Step-by-step explanation:
Let x represent the cost of a chicken sandwich.
Let y represent the cost of a large soda.
A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. This means that
4x + 5y = 22.5 - - - - - - - -1
The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. This means that
7x + 6y = 35.25 - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 4, it becomes
28x + 35y = 157.5
28x + 24y = 141
Subtracting
11y = 16.5
y = 16.5/11 = 1.5
Substituting y = 1.5 into equation 1, it becomes
4x + 5 × 1.5 = 22.5
4x + 7.5 = 22.5
4x = 22.5 - 7.5 = 15
x = 15/4 = 3.75
