Two integers have a sum of 42 and a difference of 22. the greater of the two
integers is

Let
x = larger integer
y = smaller integer

The two integers (x and y) have a sum of 42 which means they add to 42

x+y = 42

solve for y to get 

y = 42-x

simply by subtracting x from both sides



The two integers have a difference of 22. This translates to "subtract the values and the result will be 22", i.e.,

x-y = 22

Plug in y = 42-x. Solve for x

x-y = 22
x-(y) = 22
x - (42-x) = 22
x - 42 + x = 22
2x - 42 = 22
2x - 42+42 = 22+42
2x = 64
2x/2 = 64/2
x = 32

If x = 32, then y is...
y = 42-x
y = 42-32
y = 10

Therefore, 
x = 32
y = 10

The final answer is 10