Question 2245
Define...
first digit = x
second digit = y

x+y = 9 --eqn1

now for the tricky one... original number is (10x+y), so

2(10x+y) = (2(10y+x)-18 --eqn2

so expand eqn2 to give 20x+2y = 20y+2x-18

18x-18y=-18 --eqn3

sub in 3 for x (from eqn1)

18(9-y)-18y=-18
162-18y-18y=-18
-36y=180
y=5

so, x=4

CHECK!

45 doubled is 90

54 doubled is 108-18 is 90, so correct!

jon