Let's find the integers step-by-step.
1. Understanding Consecutive Integers:
- Consecutive integers are numbers that follow each other in order. For example, [tex]\( x, x+1, x+2 \)[/tex].
2. Setting Up the Problem:
- Let's assume the three consecutive integers are [tex]\( x, x+1 \)[/tex], and [tex]\( x+2 \)[/tex].
3. Formulating the Equation:
- The sum of these three integers is given as 303.
- Therefore, the equation we set up is:
[tex]\[
x + (x + 1) + (x + 2) = 303
\][/tex]
4. Simplifying the Equation:
- Combine like terms:
[tex]\[
x + x + 1 + x + 2 = 303 \implies 3x + 3 = 303
\][/tex]
5. Solving for [tex]\( x \)[/tex]:
- First, subtract 3 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
3x + 3 - 3 = 303 - 3 \implies 3x = 300
\][/tex]
- Next, divide both sides by 3:
[tex]\[
\frac{3x}{3} = \frac{300}{3} \implies x = 100
\][/tex]
6. Identifying the Consecutive Integers:
- Now that we have [tex]\( x = 100 \)[/tex], the consecutive integers are:
[tex]\[
x = 100, \quad x + 1 = 101, \quad x + 2 = 102
\][/tex]
So, the three consecutive integers whose sum is 303 are:
\[
\boxed{100, 101, 102}
