There was a total of 60 bicycles and tricycles in a shop. A bicycle has 2 wheels and a tricycle has 3 wheels. There were 156 wheels altogether.

a) How many bicycles were there?

b) How many more tricycles than bicycles where there in the shop?

Let's solve this step by step.

### Step 1: Define variables
Let:
- \( x \) be the number of bicycles in the shop.
- \( y \) be the number of tricycles in the shop.

### Step 2: Formulate the system of equations
- Since there are a total of 60 bicycles and tricycles, we have the equation:
  \[
  x + y = 60 \quad \text{(Equation 1)}
  \]
  
- Each bicycle has 2 wheels and each tricycle has 3 wheels. The total number of wheels is 156, so:
  \[
  2x + 3y = 156 \quad \text{(Equation 2)}
  \]

### Step 3: Solve the system of equations
From Equation 1, solve for \( y \) in terms of \( x \):
\[
y = 60 - x
\]

Substitute this into Equation 2:
\[
2x + 3(60 - x) = 156
\]

Simplify and solve for \( x \):
\[
2x + 180 - 3x = 156
\]
\[
-x + 180 = 156
\]
\[
-x = 156 - 180
\]
\[
x = 24
\]

So, there are 24 bicycles.

### Step 4: Find the number of tricycles
Now, substitute \( x = 24 \) into Equation 1 to find \( y \):
\[
24 + y = 60
\]
\[
y = 60 - 24
\]
\[
y = 36
\]

Thus, there are 36 tricycles.

### Part (a) Answer:
There are **24 bicycles** in the shop.

### Part (b) Answer:
To find how many more tricycles than bicycles there are:
\[
36 - 24 = 12
\]

Thus, there are **12 more tricycles than bicycles** in the shop.

Would you like more details on this solution or have any other questions?

Here are 5 related questions to expand your understanding:
1. What if there were 100 wheels altogether? How many bicycles and tricycles would be in the shop?
2. How many tricycles would there be if there were 40 bicycles in the shop?
3. If 10 more bicycles were added to the shop, how would that affect the number of wheels?
4. What if the total number of vehicles was 80 instead of 60? How would the solution change?
5. How many bicycles and tricycles would be present if the total wheels were increased to 200?

**Tip:** In problems involving multiple unknowns, defining clear variables and forming equations based on known relationships is key to solving them systematically.

Learn how to solve a system of linear equations to find the number of bicycles and tricycles in a shop. This problem involves 60 bicycles and tricycles, and 156 wheels altogether. Detailed step-by-step solution using algebraic concepts, suitable for students in Grades 6-8.

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