The sum of two numbers is 72 while the difference between the numbers is 25. the larger of the numbers is

2 equations: the first one is the sum of 2 unknown numbers x and y: x + y = 72. Now the difference is 25, so x - y = 25. Solve the first equation for y: y = 72 - x. Sub that into the second equation to solve for x: x - (72 - x) = 25. x - 72 + x = 25 and 2x - 72 = 25. Therefore, 2x = 97 and x = 48.5 That's the larger of the 2 numbers; since we subtracted y from x we defined x as the larger of the 2. Just for fun, plug x in to find that y = 23.5