Our two digit number has two digits, and let's say that T is in the tens place and U is in the units (or ones place). The number looks like this: TU
As a result, T and U are our variables.
We are told the sum of the digits is 11, so T + U = 11.
We are told the ones digit is 3 less than the tens digit. Translating that, we have U = T - 3.
We take the two equations we made and solve their system.
T + U = 11 (1)
U = T - 3 (2)
Number the equations as (1) and (2) for ease, and we solve them by substitution since (2) is solved for U; U on one side of the equals and not U on the other.
T + U = 11 <---- equation (1)
T + T - 3 = 11 <-----put (2) into (1)
2T - 3 = 11 <----collect like terms
2T = 14 <-----add 3 to both sides
T = 7 <---- divide both sides by 2
Since the sum of the digits is 11 - - our equation (1), we put T = 7 into (1)
T + U = 11
7 + U = 11
4 = U
This makes our number 74. Now let's check. The digits add to 11, 7 is odd, and the ones is less. Bingo.
Therefore the mystery number is 74.