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
\[
\boxed{5}
\]
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
\[
\boxed{5}
\]
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