Complete the steps to solve the bike-shop problem.

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?
Write your system of equations.
Fact
Equation
The number of bicycles plus the number of
1 Answer
—--=
The number of wheels on bicycles plus the
1 Answer
unicycles is 18.
number of wheels on unicycles is 28.
::2b +u=28
::b+u= 18

3 answers

To solve the bike-shop problem, we'll define our variables first:

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

Then we can formulate the system of equations based on the information provided:

  1. The total number of seats (bicycles have 2 seats each, while unicycles have 1 seat each): \[ b + u = 18 \]

  2. The total number of wheels (bicycles have 2 wheels each, while unicycles have 1 wheel each): \[ 2b + u = 28 \]

So the final set of equations for this problem is:

\[ \begin{align*}

  1. & \quad b + u = 18 \quad \text{(Equation 1)} \
  2. & \quad 2b + u = 28 \quad \text{(Equation 2)} \end{align*} \]

Now to solve the system of equations:

  1. From Equation 1, we can express \( u \) in terms of \( b \): \[ u = 18 - b \]

  2. Substitute \( u = 18 - b \) into Equation 2: \[ 2b + (18 - b) = 28 \]

  3. Simplifying this: \[ 2b + 18 - b = 28 \ b + 18 = 28 \ b = 10 \]

  4. Now substitute \( b = 10 \) back into Equation 1 to find \( u \): \[ 10 + u = 18 \ u = 18 - 10 \ u = 8 \]

Thus, the solution to the bike-shop problem is:

  • Number of bicycles \( b = 10 \)
  • Number of unicycles \( u = 8 \)

Final Answer:

  • There are 10 bicycles and 8 unicycles.
Fact
Equation
The number of bicycles plus the number of unicycles is 18.

Answer
The number of wheels on bicycles plus the number of wheels on unicycles is 28.
Answer
:: 2b +u = 28
b+u= 18
So pick one of those to go in each of the things

It seems you want to fill in the blanks according to the specific formulation of the problem. Let's directly address each statement as you indicated:

Fact

The number of bicycles plus the number of unicycles is 18.

Equation

\( b + u = 18 \)


Fact

The number of wheels on bicycles plus the number of wheels on unicycles is 28.

Equation

\( 2b + u = 28 \)

So, to summarize:

  1. Fact: The number of bicycles plus the number of unicycles is 18.

    • Equation: \( b + u = 18 \)
  2. Fact: The number of wheels on bicycles plus the number of wheels on unicycles is 28.

    • Equation: \( 2b + u = 28 \)

You can now proceed to solve these equations using the substitutions or elimination methods as shown previously! If you need further assistance, feel free to ask.