Complete the steps to solve the bike-shop problem.

Question

The owner of a bike shop sells 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?
What do you know?
A bicycle has
type your answer...
seat and type your answer...
wheels.
A unicycle has
type your answer...
seat and type your answer...
wheel.
Read the box. There are a total of type your answer...
seats and type your answer...
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• Match the ke...
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wheels.

Answer 1

To solve the bike shop problem, let's first summarize what we know about the unicycles and bicycles:

1. A bicycle has:

   • 1 seat
   • 2 wheels

2. A unicycle has:

   • 1 seat
   • 1 wheel

Now let's define our variables:

• Let \( b \) represent the number of bicycles.
• Let \( u \) represent the number of unicycles.

From the problem, we have two equations based on the counts of seats and wheels:

1. For seats: \[ b + u = 18 \] (because each cycle has 1 seat)

2. For wheels: \[ 2b + u = 28 \] (because each bicycle has 2 wheels and each unicycle has 1 wheel)

Now we can solve these equations step by step.

Step 1: Solve the first equation for \( u \): \[ u = 18 - b \]

Step 2: Substitute \( u \) in the second equation: \[ 2b + (18 - b) = 28 \] This simplifies to: \[ 2b + 18 - b = 28 \] \[ b + 18 = 28 \] \[ b = 28 - 18 \] \[ b = 10 \]

Step 3: Substitute \( b \) back to find \( u \): \[ u = 18 - 10 = 8 \]

Thus, the bike shop has:

• 10 bicycles
• 8 unicycles

In summary:

• 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.