A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the new number?

Answer 1

let the tens digit of our number be x
let the unit digit be y

so the number is 10x + y

sum of its digit = x+y

10x + y = 7(x+y) - 3
3x - 6y = -3 , #1

the number reversed is 10y+x
10y+x = 10x+y - 18
9y - 9x = -18
y - x = -2
y = x-2

sub this into #1
3x - 6(x-2) = -3
-3x = -3-12
x = 5
y = 5-2 = 3

the original number was 53
the new number is 35

check:
is 35 less than 53 by 18 ? YEAH
7 times the sum of the digits is 56
is that less than 53 by 3 ? YEAHHHH