# 5-digit Number Puzzle - Solution

## The Puzzle:

## Our Solution:

We can make an equation:

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)

10x+1 = 300000 + 3x

10x = 299999 + 3x

7x = 299999

x = 299999/7 = 42857

The answer is 42857 (142857 is three times smaller than 428571)

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)

10x+1 = 300000 + 3x

10x = 299999 + 3x

7x = 299999

x = 299999/7 = 42857

The answer is 42857 (142857 is three times smaller than 428571)