Question 134766
First, digits are the numerals 0,1,2,3,4,5,6,7,8,and 9
In a 2-digit number, the leading digit has a "place value"
of 10 times the value of the digit. The 2nd digit has
a value of 1 times it's value, so a number like
37 = 
(10 x 3) + (7 x 1) = 30 + 7
30 + 7 = 37
Call the 2-digit number in the problem {{{10a + b}}}
The digits are {{{a}}} and {{{b}}}
(1) {{{10a + b = 7b}}}
{{{10a + b + 18 = 10b + a}}}
(2) {{{9a + 18 = 9b}}}
---------------------
From (1)
{{{6b = 10a}}}
{{{b = (5/3)*a}}}
Substitute this in (2)
{{{9a + 18 = 9*(5/3)*a}}}
{{{9a + 18 = 15a}}}
{{{6a = 18}}}
{{{a = 3}}}
{{{b = (5/3)*a}}}
{{{b = 5}}}
The number is {{{10a + b}}}
{{{10a + b = 10*3 + 5}}}
{{{10*3 + 5 = 35}}} answer
Is 35 7 times its unit digit? Yes
If I add 18 are the digits reversed?
{{{35 + 18 = 53}}} Yes
OK