Bikes, Trikes and more

At Brittany's Bike shop, she rents all kinds of cycles: unicycles, tandems, regular bikes, and even tricycles. She parks all the cycles in front of her shop with a helmet for each rider strapped to the cycles. This morning Brittany counted 57 Helmets and 115 wheels. She knows she an egual number of unicycles and tandems. She also knows that she has 32 regular bikes. How many unicycles, tandems and trikes does she have.

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Write the expression in math symbols: the sum of m squared and 8

To find the number of unicycles, tandems, and trikes Brittany has, we need to analyze the given information:

1. Brittany counts 57 helmets, which means she has 57 riders in total.
2. Each cycle has a helmet, so the total number of cycles will be equal to the number of riders.
3. The total number of wheels is 115.

Let's solve this step by step:

1. We know that Brittany has an equal number of unicycles and tandems. Let's represent the number of unicycles and tandems as 'x'.
- Unicycles = x
- Tandems = x

2. We are given that Brittany has 32 regular bikes. We can represent the number of regular bikes as 'r'.
- Regular bikes = 32

3. The total number of cycles can be computed by adding the number of unicycles, tandems, and regular bikes.
- Total cycles = Unicycles + Tandems + Regular bikes = x + x + r

4. The total number of wheels can also be calculated by adding the wheels of each cycle type.
- Total wheels = (Unicycles x 1 wheel) + (Tandems x 2 wheels) + (Regular bikes x 2 wheels) + (Trikes x 3 wheels)
- 115 wheels = x + 2x + 2r + (Trikes x 3)

Now, let's substitute the known values into the equations:

From equation 1: x = number of unicycles = number of tandems
From equation 2: r = number of regular bikes = 32

Substituting these values into equation 3, we get:
Total cycles = 2x + 32

Substituting these values into equation 4, we get:
115 = x + 2x + 2(32) + (Trikes x 3)
115 = 3x + 64 + 3(Trikes)
115 - 64 = 3x + 3(Trikes)
51 = 3x + 3(Trikes)

Now, we have two variables, x (number of unicycles) and Trikes. We need another equation to solve for them.

From the given information, we know that the total number of helmets equals the total number of riders. Since each cycle has a helmet, the number of helmets is also equal to the total number of cycles.

Total cycles = x + x + r
57 = 2x + 32

Now, we have two equations:
1st equation: 2x + 32 = 57
2nd equation: 51 = 3x + 3(Trikes)

Solving these equations simultaneously will give us the values of x (unicycles) and Trikes (tricycles).

I'll solve these equations for you.