Final answer:
The system of equations for the purchases is 6c + 6s = $22 for Kate and 2c + 8s = $27 for Greg. By solving these equations, we find that one chicken sandwich costs $1.70 and one bowl of soup costs $2.95.
Step-by-step explanation:
Step-by-Step Solution to the System of Equations
Let's assign symbols to represent the cost of the items. Let c be the cost of one chicken sandwich and s be the cost of one bowl of soup.
Writing the Equations
We can write two equations based on the information given:
- For Kate's purchase: 6c + 6s = $22
- For Greg's purchase: 2c + 8s = $27
Solving the System of Equations
To solve for c and s, we can use the substitution or elimination method. For simplicity, we'll use the elimination method.
- Multiply the first equation by two: 12c + 12s = $44
- Rewrite the second equation: 2c + 8s = $27
- Subtract the second equation from the multiplied first equation: (12c + 12s) - (2c + 8s) = 10c + 4s = $17
- Divide the result by 10 to find the cost of one chicken sandwich: c = $1.70
- Substitute c = $1.70 into either original equation to find s
- Using 2c + 8s = $27: 2($1.70) + 8s = $27 leads to $3.40 + 8s = $27
- Subtract $3.40 from both sides: 8s = $23.60
- Divide both sides by 8: s = $2.95
Therefore, one chicken sandwich costs $1.70, and one bowl of soup costs $2.95.