At Irv's Cycle Rental Shop, Irv renst all knids of cycles: unicyles, tandem bikes, regualr bikes, and even tricycles for little kids. He parks all the cycles in front of the shop with a helmet for each rider strapped to the cycles. This morninf Irv counted 57 helments 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 unicycle, tandem bikes, and tricycles does Irv have?

Question

At Irv's Cycle Rental Shop, Irv renst all knids of cycles: unicyles, tandem bikes, regualr bikes, and even tricycles for little kids. He parks all the cycles in front of the shop with a helmet for each rider strapped to the cycles. This morninf Irv counted 57 helments 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 unicycle, tandem bikes, and tricycles does Irv have?

Answer 1

To find the number of unicycles, tandem bikes, and tricycles at Irv's Cycle Rental Shop, we can break down the given information and create equations to solve.

Let's represent the number of unicycles as "u", the number of tandem bikes as "t", and the number of tricycles as "c".

From the given information, we can create the following equations:

1. u + t = total number of unicycles and tandem bikes
2. u = t (since Irv has an equal number of unicycles and tandem bikes)
3. c = total number of helmets - (number of unicycles + number of tandem bikes + number of regular bikes)
= 57 - (u + t + 32)

We also know that the total number of wheels parked is 115. Since each unicycle has 1 wheel, each tandem bike has 2 wheels, each regular bike has 2 wheels, and each tricycle has 3 wheels, we can create the following equation:

4. u + 2t + 2(32) + 3c = 115

Now, we can solve these equations simultaneously to find the values of u, t, and c.

Using the equation u = t (from equation 2), we can substitute "t" for "u" in equations 1, 3, and 4:

t + t = total number of unicycles and tandem bikes
2t + 2(32) + 3c = 115
57 - (t + t + 32)

Simplifying these equations, we get:

2t = total number of unicycles and tandem bikes
2t + 2(32) + 3c = 115
25 - 2t

From the first equation, we get:

2t = total number of unicycles and tandem bikes = 25

Substituting this value in the second equation, we have:

2(25) + 2(32) + 3c = 115
50 + 64 + 3c = 115
114 + 3c = 115
3c = 115 - 114
3c = 1
c = 1/3

However, c cannot be a fraction because it represents the number of tricycles. Therefore, it must be an integer.

Since the number of regular bikes is given as 32, we can assume that the total number of bikes (including regular bikes) is greater than or equal to 32. Therefore, the minimum value for c is 0.

Therefore, c = 0.

Substituting c = 0 in the second equation:

2t + 2(32) = 115
2t + 64 = 115
2t = 115 - 64
2t = 51
t = 51/2
t = 25.5

Again, t cannot be a fraction because it represents the number of tandem bikes. Therefore, it must be an integer.

Since all the values we've calculated so far are not integers, we need to reassess our approach. It seems there might be an error or inconsistency in the given information or calculations.