Question

What 3 consecutive integers equal 84

Answer 1

27 + 28 + 29 = 84

Explanation:

Let the three consecutive integers be x +1, x+2 and x+3

Thus,

`(x + 1) + (x + 2) + (x + 3) = 84`

Remove the brackets

`x + 1 + x + 2 + x + 3 = 84`

Group the like terms

`x + x + x + 1 + 2 + 3 = 84`

`3x + 6 = 84`

To make 3x subject of formula, subtract 6 from both sides of the equation thus,

`3x + 6 - 6 = 84 - 6`

`3x = 78`

Divide through by 3

`(3x)/(3) = (78)/(3)`

`x = 26`

Since x = 26

`x + 1 = 26 + 1 = 27`

`x + 2 = 26 + 2 = 28`

`x + 3 = 26 + 3 = 29`

Therefore, the three consecutive integers are 27, 28 and 29

Check

`27 + 28 + 29 = 84`

Answer 2

First represent your 3 consecutive integers as follows.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since their sum is 84, our equation reads x + (x + 1) + (x + 2) = 84.

Simplifying on the left side we get 3x + 3 = 84.

Now subtract 3 from both sides to get 3x = 81.

Dividing both sides by 3, we find that x = 27.

Finally, make sure you list all your answers.

If x is 27 then x + 1 is 28 and x + 2 is 29.