Question 836481

let a = the 100's digit
let b = the 10's
let c = the units
then 
100a + 10b + c = "the number"
:
Write an equation for each statement:
The ten's digit of a three-digit number is twice the unit's digit.
b = 2c
or
c = .5b
The hundred's digit of the number is twice the ten's digit.
a = 2b
 The number formed by reversing the digits of the number is 594 less than it
100a + 10b + c = 100c + 10b + a + 594 
100a - a + 10b - 10b = 100c - c + 594
99a = 99c + 594
simplify, divide by 99
a = c + 6
replace a with 2b, replace c with .5b
2b = .5b + 6
2b - .5b = 6
1.5b = 6
b = 6/1.5
b = 4
then
a = 2(4)
a = 8
and
c = .5(4)
c = 2
:
the number is 842
:
 you can check this in the statement:
"The number formed by reversing the digits of the number is 594 less than it"