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?

A. Equation One is incorrect, the correct equation is e = r - 7
B. Equation Two is incorrect, the correct equation is r - e = 37
C. Equation One is incorrect, the correct equation is r = e - 7
D. The equations are set up correctly and Ms. Stewart can continue to solve the problem.

Answer 1

Ms. Stewart made an error in setting up the equations. Let's analyze the problem:

1. The statement "Reese is seven years younger than Emily" can be expressed as:
\[
r = e - 7 \quad \text{(this means Reese's age is Emily's age minus 7)}
\]

2. The statement "the sum of their ages is 37" is correctly expressed as:
\[
r + e = 37
\]

Given this, the correct first equation should be \( r = e - 7 \), not \( r = 7 - e \).

Thus, the correct answer is:
**C. Equation One is incorrect, the correct equation is r = e - 7.**