Find three consecutive numbers whose sum is 84?

Let the three consecutive numbers be \(x\), \(x+1\), and \(x+2\).

The sum of these three numbers is given by the equation:

\[
x + (x+1) + (x+2) = 84
\]

Simplifying this equation:

\[
3x + 3 = 84
\]

Subtract 3 from both sides:

\[
3x = 81
\]

Now, divide both sides by 3:

\[
x = 27
\]

Thus, the three consecutive numbers are:

\[
27, 28, 29
\]

Their sum is:

\[
27 + 28 + 29 = 84
\]

Would you like further details or have any questions?

Here are five related questions:
1. What would the numbers be if the sum was 120?
2. How do you generalize the sum of any three consecutive numbers?
3. Can you find four consecutive numbers whose sum is 110?
4. What is the formula to find the sum of \(n\) consecutive numbers?
5. How would the solution change if the numbers were consecutive odd numbers?

**Tip:** To solve problems involving consecutive numbers, setting up an equation with variables is a reliable approach!

Learn how to find three consecutive numbers whose sum is 84. This problem explores algebraic concepts and linear equations, suitable for middle school students (Grades 6-8). A detailed step-by-step solution is provided, explaining how to set up and solve the equation.

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