# The sum of two consecutive odd numbers is 52. What are the two odd numbers?explanation in detail needed!​

The sum of two consecutive odd numbers is 52. What are the two odd numbers?
explanation in detail needed!​

### 2 thoughts on “The sum of two consecutive odd numbers is 52. What are the two odd numbers?<br />explanation in detail needed!​”

First, an even number is a multiple of 2: 2, 4, 6, 8, and so on. It is conventional in algebra to represent an even number as 2n, where, by calling the variable ‘n,’ it is understood that n will take whole number values: n = 0, 1, 2, 3, 4, and so on.

An odd number is 1 more (or 1 less) than an even number. And so we represent an odd number as 2n + 1.

Let 2n + 1, then, be the first odd number. Then the next one will be 2 more — it will be 2n + 3. The problem states that their sum is 52:

2n + 1 + 2n + 3 = 52.

We will now solve that equation for n, and then replace the solution in 2n + 1 to find the first odd number. We have:

4n + 4 = 52

4n = 48

n = 12.

Therefore the first odd number is 2 · 12 + 1 = 25. And so the next one is 27. Their sum is 52.

2. $$\huge\mathbb\fcolorbox{pink}{lavenderblush}{♡ᎪղՏωᎬя᭄}$$

First, an even number is a multiple of 2: 2, 4, 6, 8, and so on. It is conventional in algebra to represent an even number as 2n, where, by calling the variable ‘n,’ it is understood that n will take whole number values: n = 0, 1, 2, 3, 4, and so on.

An odd number is 1 more (or 1 less) than an even number. And so we represent an odd number as 2n + 1.

Let 2n + 1, then, be the first odd number. Then the next one will be 2 more — it will be 2n + 3. The problem states that their sum is 52:

2n + 1 + 2n + 3 = 52.

We will now solve that equation for n, and then replace the solution in 2n + 1 to find the first odd number. We have:

4n + 4 = 52

4n = 48

n = 12.

Therefore the first odd number is 2 · 12 + 1 = 25. And so the next one is 27. Their sum is 52.