Question 503003
let x = the 10's digit
let y = the units
then
10x+y = the number
:
"a two digit number is such that it is equal to 4 times the sum of it's digits."
10x + y = 4(x+y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
simplify, divide by 2
2x = y
:
 "when 27 is added to the number the total is equal to the same number when it's digits are interchanged."
10x + y + 27 = 10y + x
10x - x + 27 = 10y - y
9x + 27 = 9y
simplify, divide by 9
x + 3 = y
Replace y with 2x, (from the 1st statement)
x + 3 = 2x
3 = 2x - x
x = 3
y = 2(3)
y = 6
and
36 is the number
:
:
Check this in the 1st statement:
a two digit number is such that it is equal to 4 times the sum of it's digits. 
36 = 4(3+6); confirms our solutions