The owner of a bike shops seems unicycles and bicycles and keeps inventory by counting seats and wheels. One day. She counts 18 seats and 28 wheels. How many of each type of cycle are there? This

Question

(Fill in the blanks)

A bicycle has 1 seat and 2 wheels. A unicycle has 1 seat and 1 wheel. There are a total of ____ seats and _____ wheels

Answer 1

Let's denote the number of bicycles as \( b \) and the number of unicycles as \( u \).

From the information given:

• A bicycle has 1 seat and 2 wheels.
• A unicycle has 1 seat and 1 wheel.

We have the following equations based on the counts of seats and wheels:

1. The total number of seats is given by: \[ b + u = 18 \quad \text{(equation 1)} \]

2. The total number of wheels is given by: \[ 2b + u = 28 \quad \text{(equation 2)} \]

Now, we can solve the system of equations.

First, let's solve equation 1 for \( u \): \[ u = 18 - b \]

Next, we can substitute \( u \) from this equation into equation 2: \[ 2b + (18 - b) = 28 \]

Now simplify: \[ 2b + 18 - b = 28 \] \[ b + 18 = 28 \] \[ b = 28 - 18 \] \[ b = 10 \]

Now we can find \( u \) using equation 1: \[ u = 18 - b = 18 - 10 = 8 \]

Thus, the owner has:

• 10 bicycles
• 8 unicycles

So, the fill-in-the-blanks would be: A bicycle has 1 seat and 2 wheels. A unicycle has 1 seat and 1 wheel. There are a total of 18 seats and 28 wheels.