Certainly! Let's solve the problem step by step to find the three consecutive positive integers whose sum is 54.
1. Define the integers:
Let the three consecutive integers be [tex]\( n \)[/tex], [tex]\( n+1 \)[/tex], and [tex]\( n+2 \)[/tex].
2. Set up the equation:
The sum of these three consecutive integers is given as 54. Therefore, we can write the equation:
[tex]\[
n + (n+1) + (n+2) = 54
\][/tex]
3. Combine like terms:
Combine the [tex]\( n \)[/tex]'s together:
[tex]\[
n + n + 1 + n + 2 = 54
\][/tex]
[tex]\[
3n + 3 = 54
\][/tex]
4. Isolate the variable [tex]\( n \)[/tex]:
To find [tex]\( n \)[/tex], we need to isolate it on one side of the equation. First, subtract 3 from both sides:
[tex]\[
3n + 3 - 3 = 54 - 3
\][/tex]
[tex]\[
3n = 51
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
Now, divide both sides by 3:
[tex]\[
\frac{3n}{3} = \frac{51}{3}
\][/tex]
[tex]\[
n = 17
\][/tex]
6. Find the consecutive integers:
Now that we have [tex]\( n \)[/tex], we can find the three consecutive integers:
[tex]\[
n = 17
\][/tex]
[tex]\[
n+1 = 17+1 = 18
\][/tex]
[tex]\[
n+2 = 17+2 = 19
\][/tex]
7. Conclusion:
Therefore, the three consecutive integers whose sum is 54 are [tex]\( 17 \)[/tex], [tex]\( 18 \)[/tex], and [tex]\( 19 \)[/tex].
So the solution to the problem is: The three consecutive integers are 17, 18, and 19.
