a two digit is such that the sum of the ones and tens digit is ten. If the digits are reversed the new number formed exceeds the original by 54. Find the number

2 answers

The digits are a and b.

The original number:

10 a + b

The reversed number:

a + 10 b

If the digits are reversed the new number formed exceeds the original by 54 means:

a + 10 b - ( 10 a + b ) = 54

a + 10 b - 10 a - b = 54

- 9 a + 9 b = 54

Now you must solve system:

a + 10 b = 10

- 9 a + 9 b = 54
____________

The solutions are:

a = 2 , b = 8

The original number:

10 a + b = 10 ∙ 2 + 8 = 20 + 8 = 28

The reversed number:

a + 10 b = 2 + 10 ∙ 8 = 2 + 80 = 82

82 - 28 = 54
28