Understanding the Problem
To find three consecutive odd numbers that sum up to 63, we first need to define the numbers. Odd numbers can be represented in a sequence where each number can be expressed in relation to the others.
Defining the Numbers
- Let the first odd number be represented as x.
- The next consecutive odd number can be expressed as x + 2.
- The third consecutive odd number can be expressed as x + 4.
Setting Up the Equation
Now, we can sum these three numbers and set it equal to 63:
- Sum of the three numbers: x + (x + 2) + (x + 4) = 63
This simplifies to:
- 3x + 6 = 63
Solving the Equation
Now, we will solve for x:
- 3x + 6 = 63
- Subtract 6 from both sides:
- 3x = 57
- Now divide by 3:
- x = 19
Finding the Consecutive Odd Numbers
With x found, we can now determine the three consecutive odd numbers:
- First number: x = 19
- Second number: x + 2 = 21
- Third number: x + 4 = 23
Conclusion
Thus, the three consecutive odd numbers that add up to 63 are:
- 19, 21, and 23.
These numbers satisfy the conditions of the problem, and their sum is confirmed to be 63.