Sure! Let's create a real-world scenario that involves a single linear equation with one solution.
Scenario:
Suppose you are saving money to buy a new laptop that costs $800. You already have $200 saved up, and you plan to save an additional $50 each month. We want to find out how many months it will take for you to reach the total amount needed to buy the laptop.
Let's Set Up the Equation:
Let \( x \) be the number of months it takes to save enough money for the laptop. The total amount saved after \( x \) months can be expressed as:
\[ 200 + 50x \]
We want this total to equal the cost of the laptop, which is $800. Therefore, we can set up the equation:
\[ 200 + 50x = 800 \]
Solving the Equation:
- Subtract 200 from both sides:
\[ 50x = 800 - 200 \]
\[ 50x = 600 \]
- Divide both sides by 50:
\[ x = \frac{600}{50} \]
\[ x = 12 \]
Conclusion:
It will take you 12 months to save enough money to buy the laptop.