Question

The sum of two consecutive integers is 59. Write an equation that models this situation and find the values of the two integers.


n + n + 1 = 59; n = 29; n + 1 = 30


n + 2n = 59; n = 19; 2n = 38


n + n + 1 = 59; n = 30; n + 1 = 31


n + n + 1 = 59; n = 29; n + 1 = 28

Answer 1

To model the situation where the sum of two consecutive integers is 59, we can use the following equation:

Let \( n \) be the first integer. Then the second consecutive integer is \( n + 1 \).

Thus, the equation is:
\[
n + (n + 1) = 59
\]

Simplifying this equation:
\[
2n + 1 = 59
\]

Now, solve for \( n \):
\[
2n = 59 - 1
\]
\[
2n = 58
\]
\[
n = 29
\]

The two consecutive integers are:
\[
n = 29 \quad \text{and} \quad n + 1 = 30
\]

So, the two consecutive integers are **29 and 30**.

The correct answer from your options is:
\[
n + n + 1 = 59; n = 29; n + 1 = 30
\]