The price for an adult carnival ticket is 6.5 more than a carnival ticket for a child. Bob takes his son to the carnival. He buys cotton candy for $10.25, and spends $55. Write and solve a linear equation to find the prices for each of their carnival tickets.

a = c+6.50

a+c+10.25 = 55.00

Now just solve for a and c.

Hmmm. I don't like the answers. Maybe I misinterpreted the problem.

Son's ticket: $X.

Bob's ticket: (x+6.5).

x + (x+6.5) + 10.25 = 55.
2x + 16.75 = 55,
2x = 38.25,
X = $19.13.

(x+6.5) = 19.13 + 6.5 = $25.63.

To find the prices for the carnival tickets, we need to set up a system of equations based on the given information.

Let's assume the price of a carnival ticket for a child is C.

According to the problem, the price for an adult carnival ticket is $6.5 more than a carnival ticket for a child. Therefore, the price of an adult carnival ticket is C + 6.5.

Bob buys cotton candy for $10.25, so this amount needs to be subtracted from the total amount spent ($55) to find the combined price of the carnival tickets.

Now, we can set up the system of equations:

Equation 1: C + (C + 6.5) = 55 - 10.25
Equation 2: C + 6.5 = C + 6.5

Simplifying Equation 1, we get:
2C + 6.5 = 44.75

Subtracting 6.5 from both sides of Equation 1, we obtain:
2C = 38.25

Finally, dividing both sides of Equation 1 by 2, we find:
C = 19.125

Thus, the price of the child's carnival ticket is $19.125.

To find the price of the adult's carnival ticket, we substitute the value of C into Equation 2:

C + 6.5 = 19.125 + 6.5
C + 6.5 = 25.625

Hence, the price of the adult's carnival ticket is $25.625.