Question 633693
The three digits: a, b, c; write an equation for each statement
Simplify each equation as much as possible
:
In a certain three digit number,
100a + 10b + c
:
 the hundreds digit is the sum of the other two digits.
a = b + c
:
If the units and tens digits of this number are interchanged,the new number
 is 9 more than the original number.
100a + 10c + b = 100a + 10b + c + 9
Subtract 100a from both sides
10c + b = 10b + c + 9
10c - c = 10b - b + 9
9c = 9b + 9
simplify, divide by 9
c = b + 1
:
If the hundreds and ten digits of the original number are interchanged,
 the new number is 360 less than the original number.
100b + 10a + c = 100a + 10b + c - 360
subtract c from both sides
100b + 10a = 100a + 10b - 360
100b - 10b = 100a - 10a - 360
90b = 90a - 360
Simplify, divide by 90
b = a - 4
or
a = b + 4
:
Using the equation: a = b + c, replace a and c
(b+4) = b + (b+1)
4 - 1 = 2b - b
3 = b
then
a = 3 + 4
a = 7
and
c = 3 + 1
c = 4
:
734 is the original number
:
You can confirm this solution in the last two statements