SOLUTION: a two digit number is such that it is equal to 4 times the sum of it's digits. when 27 is added to the number the total is equal to the same number when it's digits are interchange

Question 503003: a two digit number is such that it is equal to 4 times the sum of it's digits. when 27 is added to the number the total is equal to the same number when it's digits are interchanged. what is the number.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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

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