Question
Ms. Stewart was given the problem:
Reese is five years younger than Emily. If the sum of their ages is 32, find the age of each girl.
Ms. Stewart wrote the two equations to solve this problem. She used r for Reese's age and e for Emily's age.
Equation One:
Equation Two:
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
(1 point)
Responses
Equation One is incorrect, the correct equation is
Equation One is incorrect, the correct equation is r is equal to e minus 5
Equation One is incorrect, the correct equation is
Equation One is incorrect, the correct equation is e is equal to r minus 5
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
Equation Two is incorrect, the correct equation is
Reese is five years younger than Emily. If the sum of their ages is 32, find the age of each girl.
Ms. Stewart wrote the two equations to solve this problem. She used r for Reese's age and e for Emily's age.
Equation One:
Equation Two:
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
(1 point)
Responses
Equation One is incorrect, the correct equation is
Equation One is incorrect, the correct equation is r is equal to e minus 5
Equation One is incorrect, the correct equation is
Equation One is incorrect, the correct equation is e is equal to r minus 5
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
Equation Two is incorrect, the correct equation is
Answers
GPT-4o mini
To solve the problem about Reese and Emily's ages, let's break it down step-by-step:
1. **Understanding the Problem**:
- Reese is five years younger than Emily.
- The sum of their ages is 32.
2. **Defining Variables**:
- Let \( r \) represent Reese's age.
- Let \( e \) represent Emily's age.
3. **Setting Up Equations**:
- From the information that Reese is five years younger than Emily, we can express this relationship as:
- **Equation One**: \( r = e - 5 \)
- From the information that the sum of their ages equals 32, we can write:
- **Equation Two**: \( r + e = 32 \)
Now, looking at Ms. Stewart's setup:
- **Equation One**: Should be \( r = e - 5 \).
- **Equation Two**: Should be \( r + e = 32 \).
If Ms. Stewart used those equations correctly, then the equations are indeed set up correctly.
However, if she made a mistake in one of the equations, you would need to determine which one is incorrect based on the variable definitions.
Given that **r is Reese's age** and **e is Emily's age**, the correct interpretation is that:
- **Equation One**: \( r = e - 5 \) (this is correct, as it reflects that Reese is younger).
- **Equation Two**: \( r + e = 32 \) (this is also correct, as it sums their ages).
### Conclusion
The response stating "The equations are set up correctly and Ms. Stewart can continue to solve the problem" is correct, assuming she wrote them as \( r = e - 5 \) and \( r + e = 32 \).
If any of the options are misrepresented in the context given, please clarify, but based on the problem provided, the equations as described should be correct.
1. **Understanding the Problem**:
- Reese is five years younger than Emily.
- The sum of their ages is 32.
2. **Defining Variables**:
- Let \( r \) represent Reese's age.
- Let \( e \) represent Emily's age.
3. **Setting Up Equations**:
- From the information that Reese is five years younger than Emily, we can express this relationship as:
- **Equation One**: \( r = e - 5 \)
- From the information that the sum of their ages equals 32, we can write:
- **Equation Two**: \( r + e = 32 \)
Now, looking at Ms. Stewart's setup:
- **Equation One**: Should be \( r = e - 5 \).
- **Equation Two**: Should be \( r + e = 32 \).
If Ms. Stewart used those equations correctly, then the equations are indeed set up correctly.
However, if she made a mistake in one of the equations, you would need to determine which one is incorrect based on the variable definitions.
Given that **r is Reese's age** and **e is Emily's age**, the correct interpretation is that:
- **Equation One**: \( r = e - 5 \) (this is correct, as it reflects that Reese is younger).
- **Equation Two**: \( r + e = 32 \) (this is also correct, as it sums their ages).
### Conclusion
The response stating "The equations are set up correctly and Ms. Stewart can continue to solve the problem" is correct, assuming she wrote them as \( r = e - 5 \) and \( r + e = 32 \).
If any of the options are misrepresented in the context given, please clarify, but based on the problem provided, the equations as described should be correct.