The sum of 2 numbers is 82. their differences is 24. what are the numbers?

Let the two numbers be ( x ) and ( y ). We have the equations ( x + y = 82 ) and ( x - y = 24 ). By solving these equations, we can add them to eliminate ( y ):

( (x + y) + (x - y) = 82 + 24 ) leads to ( 2x = 106 ), so ( x = 53 ). Substituting ( x ) back into the first equation gives ( 53 + y = 82 ), resulting in ( y = 29 ). Thus, the two numbers are 53 and 29.