Question
can you make a real-world scenario linear equation only using the variable x and a one solution problem. explain the problem and your answer
Answers
GPT-4o mini
### Real-World Scenario: Saving for a Bicycle
**Problem Description:**
Imagine you want to buy a new bicycle that costs $300. You are currently saving money by doing odd jobs around your neighborhood. You decide to save a portion of your allowance each week, which is $30. Let \( x \) represent the number of weeks you plan to save.
**The Situation:**
You start with $0 saved. After \( x \) weeks of saving $30 each week, the total amount you will have saved can be represented by the equation:
\[ 30x = 300 \]
**Explanation of the Equation:**
- \( 30 \) represents the amount of money you save each week.
- \( x \) is the number of weeks you save.
- The total savings should equal the cost of the bicycle, which is $300.
### Solving the Equation
To find out how many weeks it will take for you to save enough money to buy the bicycle, we solve for \( x \):
\[
30x = 300
\]
To isolate \( x \), divide both sides by 30:
\[
x = \frac{300}{30}
\]
\[
x = 10
\]
### Conclusion:
You need to save for **10 weeks** to have enough money to buy the bicycle. This is a one-solution problem because, for each specific amount of $300, there is only one unique value of \( x \) (the number of weeks) that satisfies the equation \( 30x = 300 \).
**Problem Description:**
Imagine you want to buy a new bicycle that costs $300. You are currently saving money by doing odd jobs around your neighborhood. You decide to save a portion of your allowance each week, which is $30. Let \( x \) represent the number of weeks you plan to save.
**The Situation:**
You start with $0 saved. After \( x \) weeks of saving $30 each week, the total amount you will have saved can be represented by the equation:
\[ 30x = 300 \]
**Explanation of the Equation:**
- \( 30 \) represents the amount of money you save each week.
- \( x \) is the number of weeks you save.
- The total savings should equal the cost of the bicycle, which is $300.
### Solving the Equation
To find out how many weeks it will take for you to save enough money to buy the bicycle, we solve for \( x \):
\[
30x = 300
\]
To isolate \( x \), divide both sides by 30:
\[
x = \frac{300}{30}
\]
\[
x = 10
\]
### Conclusion:
You need to save for **10 weeks** to have enough money to buy the bicycle. This is a one-solution problem because, for each specific amount of $300, there is only one unique value of \( x \) (the number of weeks) that satisfies the equation \( 30x = 300 \).