Solving Real-World Equations: A Parking Lot Puzzle

Navigating a real-world scenario with simple algebra can be both fun and educational. In this article, we will solve a fascinating puzzle related to a parking lot. This problem involves a blend of basic arithmetic and algebra, providing readers with a hands-on exercise in problem-solving.

The Puzzle

Imagine a parking lot filled with bicycles and tricycles. The challenge is to determine the exact number of each type of vehicle, given the total number of wheels and drivers. Specifically, we know:

Each bicycle has 2 wheels. Each tricycle has 3 wheels. The total number of wheels in the parking lot is 34. The total number of drivers (or vehicles) is 14.

Solving the Puzzle

This puzzle can be solved using a system of linear equations. Let’s define:

b: the number of bicycles. t: the number of tricycles.

We can set up two equations based on the given information:

Total Number of Wheels

Since each bicycle has 2 wheels and each tricycle has 3 wheels, we can write:

2b 3t 34

Total Number of Vehicles

The total number of vehicles equals the number of bicycles and tricycles combined:

b t 14

Step-by-Step Solution

Now, let's solve the system of equations step by step.

Step 1: Express One Variable in Terms of Another

From the second equation, we can express t in terms of b:

t 14 - b

Step 2: Substitute and Simplify

Substitute t from the second equation into the first equation:

2b 3(14 - b) 34

Expand and simplify:

2b 42 - 3b 34

Combine like terms:

-b 42 34

Subtract 42 from both sides:

-b 34 - 42

Simplify:

-b -8

Multiply both sides by -1:

b 8

Step 3: Solve for the Other Variable

Substitute b 8 back into the second equation:

t 14 - 8 6

Conclusion

The solution to this puzzle is:

8 bicycles 6 tricycles

This exercise not only demonstrates the practical application of algebra but also illustrates how a well-structured equation can solve real-world problems.

Additional Insights

This type of problem can be both fun and instructive. It involves setting up a system of equations, manipulating algebraic expressions, and finally, substituting values to find the solution. Such exercises are excellent for developing problem-solving skills and reinforcing foundational mathematical concepts.

In summary, the parking lot puzzle is a simple but effective way to engage in higher-order thinking while practicing basic algebra techniques. It showcases the power of mathematical reasoning in solving practical problems.