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A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s digit are $x$ and $y$ respectively, write the linear equation representing the above statement.
Given:
A number is 27 more than the number obtained by reversing its digits.
Its unit’s and ten’s digits are $x$ and $y$ respectively.
To do:
We have to write the linear equation representing the above statement.
Solution:
Unit’s digit $= x$
Ten's digit $= y$
This implies,
The given number $= 10y+x$
The number obtained by reversing the digits $=10x+y$
The number is 27 more than the number obtained by reversing its digits.
Therefore,
$(x + 10y) - (y +10x) = 27$
$x + 10y - y - 10x = 27$
$-9x + 9y = 27$
$-9(x-y) = 27$
$x-y=-3$
$x-y+3=0$
Hence the linear equation representing the given statement is $x - y + 3 = 0$.
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