Question 150667
Let x = the 10's digit
Let y = the units digit
:
the number = (10x + y)
the reversed number = (10y + x)
"
Write an equation for each statement:
"The sum of the digits of a two-digit number is 11."
x + y = 11
or
y = 11-x
:
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
(10y+x) + 20 = 2(10x+y)
10y + x + 20 = 20x + 2y
10y - 2y + x - 20x = -20
8y - 19x = -20 
:
Find the original number.
;
Substitute (11-x) for y in the above equation:
8(11-x) - 19x = -20
88 - 8x - 19x = -20
-8x - 19x = 20 - 88
-27x = -108
x = {{{(-108)/(-27)}}}
x = +4
:
y = 11-4
y = 7
:
original number: 47
;
:
Check solution in the statement;
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
74 + 20 = 2(47); confirms our solutions