The largest of the four consecutive odd numbers whose sum is 64 is 19.
Let's break down how to arrive at this answer:
Understanding Consecutive Odd Numbers
Consecutive odd numbers follow each other in sequence, each differing by 2. For example: 1, 3, 5, 7 are consecutive odd numbers.
Solving the Problem
We can represent four consecutive odd numbers algebraically:
- First odd number: 2x + 1
- Second odd number: 2x + 3
- Third odd number: 2x + 5
- Fourth odd number: 2x + 7
Where 'x' is an integer.
According to the problem, the sum of these numbers is 64. So, we can write the equation:
(2x + 1) + (2x + 3) + (2x + 5) + (2x + 7) = 64
Solving the Equation
- Combine like terms: 8x + 16 = 64
- Subtract 16 from both sides: 8x = 48
- Divide both sides by 8: x = 6
Finding the Consecutive Odd Numbers
Now that we know x = 6, we can substitute it back into our expressions:
- First odd number: 2(6) + 1 = 13
- Second odd number: 2(6) + 3 = 15
- Third odd number: 2(6) + 5 = 17
- Fourth odd number: 2(6) + 7 = 19
Therefore, the four consecutive odd numbers are 13, 15, 17, and 19. The largest of these numbers is 19.
