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

1 answer

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.