To model the situation where the sum of two consecutive integers is 37, we can define the first integer as \( n \). The next consecutive integer would then be \( n + 1 \).
So, the equation we can write is:
\[ n + (n + 1) = 37 \]
Simplifying this equation:
\[ n + n + 1 = 37 \] \[ 2n + 1 = 37 \]
Next, we can solve for \( n \):
\[ 2n = 37 - 1 \] \[ 2n = 36 \] \[ n = 18 \]
Now, to find the two consecutive integers, we calculate the second integer:
\[ n + 1 = 18 + 1 = 19 \]
Thus, the two consecutive integers are \( 18 \) and \( 19 \).
The correct statement from your options is:
- n + n + 1 = 37; n = 18; n + 1 = 19.