SOLUTION: I do not understand this problem . Please help ! A two digit number is 7 times its unit digit. If 18 is added to the number, its digits are reversed. Find the number.

Question 134766: I do not understand this problem . Please help !
A two digit number is 7 times its unit digit. If 18 is added to the number, its digits are reversed. Find the number.
Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12569) (Show Source):
You can put this solution on YOUR website!
The 10 is a multiplier for the tens digit value. This problem 's answer is 35 & the when 18 is added the numbers reverse thus: 35+18=53
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10x+y=7y or 10x=7y-y or 10x=6y or x=6y/10
now replace x in the other equation & solve for y
10x+y+18=10y+x
6y+y+18=10y+6y/10
7y-10y-6y/10=-18
-3y-6y/10=-18
(-3y*10-6y)/10=-18
-30y-6y=-18*10
-36y=-180
y=-180/-36
y=5 answer.
10x=6*5
10x=30
x=30/10
x=3 answer.
proof:
10x+y=7y
10*3+5=7*5
30+5=35
35=35

Answer by josmiceli(6786) (Show Source):
You can put this solution on YOUR website!
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
The digits are and
(1)

(2)
---------------------
From (1)

Substitute this in (2)

The number is

answer
Is 35 7 times its unit digit? Yes
If I add 18 are the digits reversed?
Yes
OK