Question
Ms. Stewart was given the problem:
Reese is five years younger then 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: r = 5 - e
Equation Two: r + e = 32
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
A. Equation One is incorrect, the correct equation is e = r - 5
B. The equations are set up correctly and Ms. Stewart can continue to solve the problem.
C. Equation Two is incorrect, the correct equation is r - e = 32
D. Equation One is incorrect, the correct equation is r = e - 5
Reese is five years younger then 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: r = 5 - e
Equation Two: r + e = 32
Did Ms. Stewart make a mistake when setting up these equations? If so, which equation is incorrect and why?
A. Equation One is incorrect, the correct equation is e = r - 5
B. The equations are set up correctly and Ms. Stewart can continue to solve the problem.
C. Equation Two is incorrect, the correct equation is r - e = 32
D. Equation One is incorrect, the correct equation is r = e - 5
Answers
GPT-4o mini
Yes, Ms. Stewart made a mistake when setting up the equations.
The problem states that Reese is five years younger than Emily. This means that if we let \( e \) represent Emily's age and \( r \) represent Reese's age, we would express Reese's age in terms of Emily's age as follows:
\[ r = e - 5 \]
This indicates that Reese's age is Emily's age minus five.
Ms. Stewart wrote:
\[ r = 5 - e \]
This equation is incorrect because it implies that Reese's age is five years minus Emily's age instead of Emily's age minus five.
Therefore, the correct answer is:
**D. Equation One is incorrect, the correct equation is r = e - 5.**
Equation Two, \( r + e = 32 \), is correct and states that the sum of their ages is 32.
The problem states that Reese is five years younger than Emily. This means that if we let \( e \) represent Emily's age and \( r \) represent Reese's age, we would express Reese's age in terms of Emily's age as follows:
\[ r = e - 5 \]
This indicates that Reese's age is Emily's age minus five.
Ms. Stewart wrote:
\[ r = 5 - e \]
This equation is incorrect because it implies that Reese's age is five years minus Emily's age instead of Emily's age minus five.
Therefore, the correct answer is:
**D. Equation One is incorrect, the correct equation is r = e - 5.**
Equation Two, \( r + e = 32 \), is correct and states that the sum of their ages is 32.