# The sum of the digits of a two digit number is 9.if the digits of the numbers are reversed the new number is decreased by 9.find the number

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by Pha

Can you explain the 3rd and 4th step

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by Pha

Can you explain the 3rd and 4th step

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Let the digits are x and y.

the number will be 10x+y.

sum of digits = 9

x + y = 9

x = 9-y

if digits are reversed, the new number will be 10y+x

(10x+y) - 9 = 10y+x

⇒ 10x + y - 9 - 10y - x = 0

⇒ 10x - x + y - 10y - 9 = 0

⇒ 9x - 9y - 9 = 0

⇒ 9(x - y - 1) = 0

⇒ x - y - 1 = 0

⇒ 9 - y - y - 1 = 0

⇒ -2y + 8 = 0

⇒ 2y = 8

⇒ y = 4

x = 9-y = 9-4 = 5

The number is 10x+y = 10×5+4 = 54

the number will be 10x+y.

sum of digits = 9

x + y = 9

x = 9-y

if digits are reversed, the new number will be 10y+x

(10x+y) - 9 = 10y+x

⇒ 10x + y - 9 - 10y - x = 0

⇒ 10x - x + y - 10y - 9 = 0

⇒ 9x - 9y - 9 = 0

⇒ 9(x - y - 1) = 0

⇒ x - y - 1 = 0

⇒ 9 - y - y - 1 = 0

⇒ -2y + 8 = 0

⇒ 2y = 8

⇒ y = 4

x = 9-y = 9-4 = 5

The number is 10x+y = 10×5+4 = 54