Question

The sum of two consecutive integers is 37. Write an equation that models this situation and find the values of the two integers.


n + n + 1 = 37; n = 18; n + 1 = 19


n + n + 1 = 37; n = 19; n + 1 = 20


n + n + 1 = 37; n = 18; n + 1 = 17


n + 2n = 37; n = 12; 2n = 24

Answer 1

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**.