https://file.aiquickdraw.com/mathbot/file/1725645245839a4nmi2cw.jpg

The problem described in the image seems to be about a parking lot with 55 total spots, filled with either cars or bikes. It mentions that each car takes up 4 spaces, while each bike occupies 2 spaces, and the total number of wheels in the lot is 180. The goal is to calculate how many cars and how many bikes are in the parking lot.

We can break this into a system of equations:

Let:
- \( c \) be the number of cars.
- \( b \) be the number of bikes.

### Step 1: Equation for the total number of vehicles
Since there are 55 total vehicles:
\[
c + b = 55
\]

### Step 2: Equation for the total number of wheels
Each car has 4 wheels, and each bike has 2 wheels. The total number of wheels is 180:
\[
4c + 2b = 180
\]

### Step 3: Solve the system of equations

We can solve this system by substitution or elimination. I'll proceed with the solution.The solution to the system of equations is:

- Number of cars: \( c = 35 \)
- Number of bikes: \( b = 20 \)

Thus, there are 35 cars and 20 bikes in the parking lot.

Would you like more details on the solution, or do you have any questions? Here are 5 related questions to explore:

1. What if the total number of parking spots changes? How does that affect the solution?
2. How would the answer change if each car occupied 3 spaces instead of 4?
3. What if the number of wheels was 200 instead of 180?
4. How can we solve this problem using matrix methods?
5. Can this system of equations be represented graphically, and how?

**Tip:** Always start solving word problems by clearly defining your variables and setting up the corresponding equations.

A car park has 55 parking bays. Each bay can hold either a car or a bike. One day it is noted that every bay is occupied and the total number of wheels is 180. Calculate how many cars and how many bikes are in the car park using algebraic methods.

Learn how to solve an algebraic word problem where a parking lot has 55 parking bays filled with cars and bikes, and the total number of wheels is 180. This detailed step-by-step solution covers key algebra concepts, including setting up and solving a system of linear equations. Suitable for Grades 7-10.

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