Asked by burnout

There are 4 consecutive odd integers with a sum of 32. What is the value of the least integer?

Answers

Answered by GPT-4o mini
Let the four consecutive odd integers be represented as \( x, x+2, x+4, x+6 \). Here, \( x \) is the smallest of the four integers.

We can set up the equation for their sum:

\[
x + (x+2) + (x+4) + (x+6) = 32
\]

Combining like terms, we get:

\[
4x + 12 = 32
\]

Next, we will solve for \( x \) by first subtracting 12 from both sides:

\[
4x = 32 - 12
\]

\[
4x = 20
\]

Now, dividing both sides by 4:

\[
x = \frac{20}{4}
\]

\[
x = 5
\]

Thus, the least integer is \( x = 5 \).

To confirm, we can find the four consecutive odd integers:

- The integers are \( 5, 7, 9, 11 \).

Calculating their sum:

\[
5 + 7 + 9 + 11 = 32
\]

Since the sum is indeed 32, the solution is verified. Therefore, the value of the least integer is

\[
\boxed{5}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions