Question

find the number:
it only has 2 different digits, but they repeat.
the digits appear in the same order in both periods.
the sum of the digits is 20.
the ones digit is 5 more than the tens digit.
the number is??

clue: in math a period is group of 3 digits.

Answer 1

let's call the digits a and b, a is ones, b is tens
the number will look something like: aba,aba
the sum of all the digits is 20
a + b + a + a + b + a = 20
4a + 2b = 20
2a + b = 20

b is 5 more than a
b = a + 5

2a + (a + 5) = 20 (because b=a+5)
3a + 5 = 20
3a = 15
a = 5

then go back to one of our equations from before to find b:
a + b + a + a + b + a = 20
5 + b + 5 + 5 + b + 5 = 20
b + b = 0
2b = 0
b = 0

therefore the number is 505,505