the sum of the digits of a two number is 9 . also ,nine times this number is twice the number obtained by reversing the order of the digits. find the number
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Answer:
Step-by-step explanation:
x + y = 9 -------- 1
tens ones
x y
10x + y = 9 = original number
9 ( 10 x + y ) = 2 ( 10 y + x ) --- reversed number
90x + 9y = 20y + 2x
90x - 2x = 20y - 9 y
88x = 11y
88x - 11y = 0
11 ( 8x - y ) = 0
8x - y = 0 --------- 2
x + y = 9
8x - y = 0
9x = 9
x = 1
x + y = 9
1 + y = 9
y = 8
10(1+ 8 = 10 + 8 = 81 ------ original number
reversed number 10 ( 8 ) + 1 = 80 + 1 = 81
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18
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