Asked by Anonymous
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
Answers
Answered by
Bosnian
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
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
Answered by
JOHN
28
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