The sum of two numbers is 51 and the difference is 25. what are the numbers? larger number: smaller number:

Sum is addition: X +Y = 51

Difference is subtraction: x -y = 25

Rewrite the second equation as x-25 = y

Replace y in the first equation with x-25:

x + x-25 = 51

Simplify:

2x -25 = 51

Add 25 to each side:

2x = 76

Divide both sides by 2:

X = 76/2

X = 38

Replace x in the first equation and solve for y:

38 + y = 51

y = 51-38

y = 13

So 38 + 13 = 561 and 38 -13 = 25

Large number = 38

Small number = 13