Question

1. what is the smallest of three consecutive odd integers that have a total sum of 51?

type a response

Explanation:

Step1: Define the three consecutive odd integers

Let the smallest odd integer be \( x \). Then the next consecutive odd integer is \( x + 2 \) (since odd integers are 2 units apart), and the third one is \( x + 4 \).

Step2: Set up the equation for the sum

The sum of the three integers is 51, so we write the equation:
\( x + (x + 2) + (x + 4) = 51 \)

Step3: Simplify and solve the equation

First, combine like terms:
\( 3x + 6 = 51 \)

Subtract 6 from both sides:
\( 3x = 51 - 6 \)
\( 3x = 45 \)

Divide both sides by 3:
\( x = \frac{45}{3} \)
\( x = 15 \)

Answer:

15