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?

1 Answer
Feb 21, 2017

=75=75

Explanation:

We can also write

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

And also

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

By simpifying EQ(1) we get

9x-9y=189x9y=18

or

9(x-y)=189(xy)=18

or

x-y=18/9xy=189

or

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

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

x+y+x-y=14x+y+xy=14

or

2x=142x=14

or

x=14/2x=142

or

x=7x=7

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

7-y=27y=2

or

y=7-2y=72

or

y=5y=5

Therefore the Number is 10x+y=7510x+y=75