When you reverse the digits in a certain two-digit number, you decrease its value by 18. What is the number is the sum of its digits is 4?

1 Answer
Konstantinos Michailidis
Oct 2, 2015

It is 1313

Explanation:

Let xx and (4-x)(4−x) represent the unit and tens digits of this certain two-digit number

10*(4-x)+x=10*x+(4-x)-18=> 40-10x+x=10x+4-x-18=> 40+18-4=10x+10x-2x=> 54=18x=>x=310⋅(4−x)+x=10⋅x+(4−x)−18⇒40−10x+x=10x+4−x−18⇒40+18−4=10x+10x−2x⇒54=18x⇒x=3

Hence the unit digit is 3 the tens unit is 1.So the number is 13.

Check :31-13=1831−13=18

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