Solving Algebraic Word Problems: A Bus and Train Scenario

Algebraic word problems are an important part of understanding mathematical concepts. They often require the application of algebraic techniques to find solutions to real-world scenarios. In this article, we will explore algebraic word problems related to buses and trains. Focusing on clear and concise language, we will use equations to solve these problems and provide step-by-step explanations.

Problem 1: A Bus Scenario

A bus had some people on it initially. At the first stop, half of the people got off, and then 11 people got on. Now, there are 20 people on the bus. How many people were on the bus initially?

Step-by-Step Solution:

Let's denote the initial number of people on the bus as x.

The number of people remaining on the bus after half got off is: 1/2x. Then, 11 people got on the bus, so the total number of people on the bus becomes: 1/2x 11. After these changes, there are 20 people on the bus: 1/2x 11 20.

Now, let's solve for x:

Subtract 11 from both sides: 1/2x 20 - 11. This simplifies to: 1/2x 9. Multiply both sides by 2 to find x: x 9 × 2. This gives us: x 18.

Therefore, there were 18 people on the bus initially.

Problem 2: A Train Scenario

Another scenario involves a train. Sixty-five people started on the train.

Step-by-Step Solution:

The initial number of people on the train is given as 65. There's no mention of any stops where people got off or on, implying the train's initial number of people remains the same.

The number of people on the train initially is: 65 people.

Problem 3: Another Bus Scenario

In this scenario, eighty people were on the bus originally. At the first stop, 20 people got off, and 10 more got on. We need to find out how many people were on the bus initially.

Step-by-Step Solution:

Let P be the number of people on the bus originally.

The premise is given as:

P - 20 - 10 70 (where 20 people got off, and 10 got on).

Let's solve for P.

Combine the terms: P - 30 70. Add 30 to both sides: P 70 30. This gives us: P 100.

Therefore, there were 100 people on the bus initially.

Conclusion

Algebraic word problems can appear complex, but by breaking them down step-by-step, we can find the solutions easily. Understanding and solving these problems helps in developing logical reasoning and problem-solving skills. Whether it's a bus or a train, the underlying algebraic techniques remain the same.