Turning a real-world scenario into a linear equation might seem tough at first, but it’s actually pretty simple. Let’s break it down step by step.

Step 1: Understand the Scenario

Start by really reading the problem. Figure out what numbers you have and what you need to find.

For example, imagine you're buying notebooks and pens. Notebooks cost $2 each, and pens cost$1 each. You want to spend a total of $20.

Step 2: Define Variables

Now, let’s decide on some letters to represent what we're talking about. In this case:

• Let $n$ stand for the number of notebooks.
• Let $p$ stand for the number of pens.

Step 3: Set Up the Equation

Next, we can write an equation from the information we have. The cost of notebooks is $2n$, and the cost of pens is $1p$. Since everything together costs $20, we can write:

$$2n + 1p = 20$$

Step 4: Solve the Equation

Now it’s time to solve the equation for the variables. For example, if you decide to buy 5 notebooks, replace $n$ with 5:

$$2(5) + 1p = 20$$

This simplifies to:

$$10 + p = 20$$

So, $p = 10$. This means you can buy 10 pens!

Example Breakdown

Let’s look at another example. Say you earn $15 every hour at your part-time job, and you want to save$300 for a new bike. How many hours do you need to work?

1. Define the variable: Let $h$ be the number of hours you work.

2. Set up the equation:

   $$15h = 300$$

3. Solve:

   $$h = \frac{300}{15} = 20$$

By following these steps, you can easily turn real-life problems into linear equations. This makes solving word problems a lot easier!