Let's set up a system of equations to solve this problem.
Let C be the cost of a candy bar in dollars and S be the cost of a soda in dollars. We have two pieces of information:
1. Two candy bars and a soda cost $2.80, which can be expressed as:
2C + S = 2.80
2. A candy bar and three sodas cost $5.15, which can be expressed as:
C + 3S = 5.15
Now, we can use these equations to find the values of C and S.
First, let's solve equation 1 for S:
S = 2.80 - 2C
Now, substitute this expression for S into equation 2:
C + 3(2.80 - 2C) = 5.15
Now, solve for C:
C + 8.40 - 6C = 5.15
Combine like terms:
-5C + 8.40 = 5.15
Subtract 8.40 from both sides:
-5C = 5.15 - 8.40
-5C = -3.25
Now, divide by -5 to find the value of C:
C = -3.25 / -5
C = 0.65
Now that we know the cost of a candy bar (C) is $0.65, we can find the cost of a soda (S) using the first equation:
2C + S = 2.80
2(0.65) + S = 2.80
1.30 + S = 2.80
Subtract 1.30 from both sides to find the cost of a soda (S):
S = 2.80 - 1.30
S = 1.50
Now, we have found that a candy bar costs $0.65, and a soda costs $1.50.
To find the price difference between a soda and a candy bar, subtract the candy bar price from the soda price:
Price difference = $1.50 - $0.65 = $0.85
The price difference between a soda and a candy bar is $0.85.