Answer:
262 and 263 are consecutive natural numbers whose sum is 525.
Step-by-step explanation:
Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (
,
) We can interpret the statement mathematically by means of the following expression:
![x + y = 525](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%20525)
![x = n](https://tex.z-dn.net/?f=x%20%3D%20n)
![y = n+1](https://tex.z-dn.net/?f=y%20%3D%20n%2B1)
Where
,
,
.
This system is reduced to a single equation and solved afterwards:
![n +(n+1) = 525](https://tex.z-dn.net/?f=n%20%2B%28n%2B1%29%20%3D%20525)
![2\cdot n + 1 = 525](https://tex.z-dn.net/?f=2%5Ccdot%20n%20%2B%201%20%3D%20525)
![2\cdot n = 524](https://tex.z-dn.net/?f=2%5Ccdot%20n%20%3D%20524)
![n = 262](https://tex.z-dn.net/?f=n%20%3D%20262)
Now we evaluate
and
to obtain the natural numbers:
![x = 262](https://tex.z-dn.net/?f=x%20%3D%20262)
![y = 263](https://tex.z-dn.net/?f=y%20%3D%20263)
262 and 263 are consecutive natural numbers whose sum is 525.