Question 420199
The sum of the digits of a two-digit number is 7.
 With the digits reversed the number is 5 times the tens digit of the original number.
 Find the original number. 
:
Let x = the 10's digit
Let y = the units
then
10x + y = the original number
:
"The sum of the digits of a two-digit number is 7."
x + y = 7
x = (7-y); use this form for substitution
:
"With the digits reversed the number is 5 times the tens digit of the original"
10y + x = 5x
10y = 5x - x
10y = 4x
Substitute (7-y) for x
10y = 4(7-y)
10y = 28 - 4y
10y + 4y = 28
14y = 28
y = 28/14
y = 2
then 
7 - 2 = 5 is x
:
52 is the original number