To find the three consecutive positive integers that sum up to 54, let's denote them as [tex]\( x \)[/tex], [tex]\( x+1 \)[/tex], and [tex]\( x+2 \)[/tex].
1. Set up the equation:
- The sum of these three integers is [tex]\( x + (x+1) + (x+2) \)[/tex].
2. Combine like terms:
- Combine the terms within the equation:
[tex]\[
x + (x+1) + (x+2) = 54
\][/tex]
[tex]\[
x + x + 1 + x + 2 = 54
\][/tex]
[tex]\[
3x + 3 = 54
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Isolate [tex]\( 3x \)[/tex] by subtracting 3 from both sides of the equation:
[tex]\[
3x + 3 - 3 = 54 - 3
\][/tex]
[tex]\[
3x = 51
\][/tex]
- Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{3x}{3} = \frac{51}{3}
\][/tex]
[tex]\[
x = 17
\][/tex]
4. Determine the consecutive integers:
- The first integer is [tex]\( x = 17 \)[/tex].
- The second integer is [tex]\( x + 1 = 17 + 1 = 18 \)[/tex].
- The third integer is [tex]\( x + 2 = 17 + 2 = 19 \)[/tex].
Hence, the three consecutive positive integers are [tex]\( 17 \)[/tex], [tex]\( 18 \)[/tex], and [tex]\( 19 \)[/tex], whose sum is indeed 54.
