A number consist of two digits whose sum is 9.  If 27 is subtracted from the number it's digits are reversed.  Find the number?

Asked by SAKE | 27th Jun, 2017, 08:51: PM

Expert Answer:

begin mathsize 20px style Let space the space unit apostrophe straight s space digit space be space straight x space and space the space ten apostrophe straight s space digit space be space straight y.
Given space that space straight x plus straight y equals 9 space space space.... left parenthesis straight i right parenthesis
So comma space the space number space is space 10 straight x plus straight y.
If space 27 space is space subtracted space from space the space number comma space its space digit apostrophe straight s space are space reversed.
So comma space we space have
10 straight x plus straight y minus 27 equals 10 straight y plus straight x
rightwards double arrow 9 straight x minus 9 straight y equals 27
rightwards double arrow straight x minus straight y equals 3 space space.... left parenthesis ii right parenthesis
Adding space space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
2 straight x equals 12
rightwards double arrow straight x equals 6
Substituting space straight x equals 6 space in space left parenthesis straight i right parenthesis comma space we space get space straight y equals 3.
Hence comma space the space number space is space 63.

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Answered by Rebecca | 28th Jun, 2017, 04:17: AM

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