Question 481455
Let x = the 10's digit, Let y = units
then
10x+y is the two digit number
and
10y+x is the number reversed
:
Write an equation for each statement:
:
"two digit number is 4 times the sum of its digits,"
10x + y = 4(x+y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
Simplify, divide both sides by 2
2x = y
:
"if the number is doubled and then decreased by 12, the result is the number with the digits reversed. 
2(10x+y) - 12 = 10y + x
20x + 2y - 12 = 10y + x
20x - x = 10y - 2y + 12
19x = 8y + 12
Replace y with 2x (from the 1st equation)
19x = 8(2x) + 12
19x = 16x + 12
19x - 16x = 12
3x = 12
x = 4 is the 10's digit
and
y = 2(4)
y = 8 is the units
therefore 
48 is the number
:
You can confirm this by using 48 as the number in both statements