The sum of the digits of a two digit number is 12. When the digits are reversed the new number is 18 less than the original number. How do you find the original number?

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Answer 1 · 2015-09-24T21:41:07

Express as two equations in the digits and solve to find original number #75#.

Suppose the digits are #a# and #b#.

We are given:

#a + b = 12#

#10a + b = 18 + 10 b + a#

Since #a+b = 12# we know #b = 12 - a#

Substitute that into #10 a + b = 18 + 10 b + a# to get:

#10 a + (12 - a) = 18 + 10 (12 - a) + a#

That is:

#9a+12 = 138-9a#

Add #9a - 12# to both sides to get:

#18a = 126#

Divide both sides by #18# to get:

#a = 126/18 = 7#

Then:

#b = 12 - a = 12 - 7 = 5#

So the original number is #75#