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 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 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 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 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 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 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 a mistake when setting up the equations. The correct interpretation of the first piece of information, "Reese is seven years younger than Emily," means that if Emily's age is represented by \( e \), then Reese's age \( r \) can be represented as:
\[ r = e - 7 \]
Ms. Stewart wrote it as:
\[ r = 7 - e \]
Which is incorrect.
The second equation \( r + e = 37 \) is correct because it correctly represents the sum of their ages.
Therefore, the correct response is:
**Equation One is incorrect, the correct equation is r=e−7.**
\[ r = e - 7 \]
Ms. Stewart wrote it as:
\[ r = 7 - e \]
Which is incorrect.
The second equation \( r + e = 37 \) is correct because it correctly represents the sum of their ages.
Therefore, the correct response is:
**Equation One is incorrect, the correct equation is r=e−7.**