When you reverse the digits in a certain two-digit number you decrease its value by 18. What is the number if the sum of its digits is 12?

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Answer 1 · 2017-02-21T09:08:31

#=75#

We can also write

#(10x+y)-(10y+x)=18# ---------------EQ(1)

And also

#x+y=12# ------------------------------EQ(2)

By simpifying EQ(1) we get

#9x-9y=18#

or

#9(x-y)=18#

or

#x-y=18/9#

or

#x-y=2#--------------------------------------EQ(3)

By adding up EQ(2) and EQ(3) we get

#x+y+x-y=14#

or

#2x=14#

or

#x=14/2#

or

#x=7#

By plugging the value of #x# in the EQ(3) we get

#7-y=2#

or

#y=7-2#

or

#y=5#

Therefore the Number is #10x+y=75#