Question
Ms. Stewart was given the problem:
Reese is seven years younger than Emily. If the sum of their ages is 37, 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: r=7−e
Equation Two: r+e=37
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
(1 point)
Responses
Equation Two is incorrect, the correct equation is r−e=37
Equation Two is incorrect, the correct equation is r minus e is equal to 37
Equation One is incorrect, the correct equation is e=r−7
Equation One is incorrect, the correct equation is e is equal to r minus 7
Equation One is incorrect, the correct equation is r=e−7
Equation One is incorrect, the correct equation is r is equal to e minus 7
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
Reese is seven years younger than Emily. If the sum of their ages is 37, 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: r=7−e
Equation Two: r+e=37
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
(1 point)
Responses
Equation Two is incorrect, the correct equation is r−e=37
Equation Two is incorrect, the correct equation is r minus e is equal to 37
Equation One is incorrect, the correct equation is e=r−7
Equation One is incorrect, the correct equation is e is equal to r minus 7
Equation One is incorrect, the correct equation is r=e−7
Equation One is incorrect, the correct equation is r is equal to e minus 7
The equations are set up correctly and Ms. Stewart can continue to solve the problem.
Answers
GPT-4o mini
Ms. Stewart made an error in Equation One. The relationship states that Reese is seven years younger than Emily, which means that if \( e \) is Emily's age, then Reese's age \( r \) can be expressed as:
\[ r = e - 7 \]
However, Ms. Stewart wrote Equation One as:
\[ r = 7 - e \]
This is incorrect because it does not represent Reese being younger than Emily correctly.
Equation Two is correctly set up as:
\[ r + e = 37 \]
Thus, the correct response would be:
**Equation One is incorrect, the correct equation is \( r = e - 7 \).**
\[ r = e - 7 \]
However, Ms. Stewart wrote Equation One as:
\[ r = 7 - e \]
This is incorrect because it does not represent Reese being younger than Emily correctly.
Equation Two is correctly set up as:
\[ r + e = 37 \]
Thus, the correct response would be:
**Equation One is incorrect, the correct equation is \( r = e - 7 \).**