Two numbers total 53 and have a difference of 25. find the two numbers.

Two numbers (x + y) equal (=) 53
and
have a difference (x - y) of (=) 25.

So, x + y = 53 and x - y = 25.

Solve one equation for a variable. We'll solve for x in the first equation.

x + y = 53   Subtract y from both sides
     x = 53 - y

Substitute x for (53 - y) in the second equation.

        x - y = 25     Substitute (53 - y) in the x spot
53 - y - y = 25     Combine like terms (-y and -y)
   53 - 2y = 25     Subtract 53 from both sides
          -2y = -28   Divide both sides by -2
             y = 14

Now, find x by plugging this y-value (14) into the first equation.

  x + y = 53   Substitute y for 14
x + 14 = 53   Subtract 14 from 53
       x = 39

Check both of your answers by plugging them into the original equations.

    x + y = 53   Plug in your numbers (39 and 14)
39 + 14 = 53   Add
       53 = 53

    x - y = 25   Plug in your numbers (39 and 14)
39 - 14 = 25   Subtract
      25 = 25

So, your answers are x = 39 and y = 14 .