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.