Question

3.
The sum of two consecutive integers is 37. Write an equation that models this situation and find the values of the two integers.

Answer 1

Let the first integer be \( x \). Since we are looking for two consecutive integers, the second integer can be expressed as \( x + 1 \).

According to the problem, the sum of these two integers is 37. We can write the equation as follows:

\[
x + (x + 1) = 37
\]

Simplifying the equation:

\[
2x + 1 = 37
\]

Next, we subtract 1 from both sides:

\[
2x = 36
\]

Now, divide both sides by 2:

\[
x = 18
\]

Thus, the first integer is \( 18 \), and the second integer, being consecutive, is:

\[
x + 1 = 19
\]

Therefore, the two consecutive integers are **18 and 19**.