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

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
Equation Two is incorrect, the correct equation is r minus e is equal to 32

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

Answer 1

To solve the problem, let's set up the equations based on the statements given:

1. **Reese is five years younger than Emily** can be translated into the equation:
\[ r = e - 5 \]
(where \( r \) is Reese's age and \( e \) is Emily's age).

2. **The sum of their ages is 32** can be translated into the equation:
\[ r + e = 32 \]

Now let's see if Ms. Stewart's equations are correct based on this setup:

- **Equation One** (which should correspond to "Reese is five years younger than Emily") should be:
\[ r = e - 5 \] (this is correct)

- **Equation Two** (which should correspond to "the sum of their ages is 32") should be:
\[ r + e = 32 \] (this is also correct)

Given these equations, we conclude that:

**The equations are set up correctly and Ms. Stewart can continue to solve the problem.**