Question

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

Answer 1

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

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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

Answer 2

the greatest integer is 32.

Explanation:

Let the integers be x and y.

The sum of these integers is 42. Hence, the equation is

x + y = 42....(i)

Now, the difference is 22. Hence, second equation is

x - y = 22 ....(ii)

Add (i) and (ii)

2x = 64

Divide both sides by 2

x = 32

Plugging this value of x in (i)

32 + y = 42

y = 42 - 32

y = 10

Therefore, the greatest integer is 32.