At Irv's Rental Shop, Irv rents all kinds of cycles: unicycles, tandem bikes, regular bikes, and even tricycles for little kids. He parks all the cycles in front of his shop with a helmet for each rider strapped to the cycles. This morning Irv counted 57 helmets and 115 wheels parked in front of his store. He knows he has an equal number of unicycles and tandem bikes. He also knows that he has 32 regular bikes. How many unicycles, tandem bikes, and tricycle does Irv have?

unicycles:
tandem bikes:
tricycles:

To find the number of unicycles, tandem bikes, and tricycles, we need to use the given information.

Let's assume the number of unicycles is U, the number of tandem bikes is T, and the number of tricycles is C.

Given information:
1. There is an equal number of unicycles and tandem bikes.
2. There are 32 regular bikes.
3. There are 57 helmets and 115 wheels in total.

From the first piece of information, we can write an equation: U = T.

From the second piece of information, we know there are 32 regular bikes. Regular bikes have 2 wheels, so the total number of wheels from regular bikes is 32 * 2 = 64.

From the third piece of information, we know there are 57 helmets. As each cycle needs one helmet, we can conclude that the number of cycles is 57.

Now, let's write an equation for the total number of wheels:
2U + 2T + 3C = 115 (since each unicycle and tandem bike has 2 wheels, and each tricycle has 3 wheels)

Now, we have a system of equations:
U = T
2U + 2T + 3C = 115
U + T + C = 57
Regular bikes: 32

To solve this system, we can substitute U with T in the third equation:

T + T + C = 57
2T + C = 57

Now, let's substitute T with U in the second equation:
2U + 2U + 3C = 115
4U + 3C = 115

Using these two equations, we can solve for U and C:

(2T + C = 57) - (4U + 3C = 115)
2T - 4U + (C - 3C) = 57 - 115
2(T - 2U) = -58
T - 2U = -29 (divided by 2)

Now we have the following equations:
T - 2U = -29
4U + 3C = 115

Since there is no information about the value of U or T separately, we cannot find precise values for the number of unicycles and tandem bikes. However, we can express the solution in terms of U and C.

To simplify the equations, let's multiply the first equation by 4:
4T - 8U = -116

Now let's add this equation to the second equation:
4T + 3C - 8U = 115 - 116
3C - 8U = -1

Now we have a simplified system of equations:
3C - 8U = -1
T - 2U = -29

From here, we can express T in terms of U:
T = -29 + 2U

And express C in terms of U:
3C = -1 + 8U
C = (-1 + 8U) / 3

Now, we can express the number of cycles in terms of U:

Unicycles (U) = U
Tandem bikes (T) = -29 + 2U
Tricycles (C) = (-1 + 8U) / 3

However, without more information, we cannot determine the exact values of U, T, and C.