Question

What is the smallest number for three consecutive even integers whose sum is 28?

Answer 1

See a solution process below:

Explanation:

First, let's call the smallest number `n`

Then, because they are consecutive even numbers we can add `2` and `4` to `n` to name the other two numbers:

• `n + 2`

• `+ 4`

Now, we can write this equation and solve for `n`:

`n + (n + 2) + (n + 4) = 90`

`n + n + 2 + n + 4 = 90`

`n + n + n +2 + 4 = 90`

`1n + 1n + 1n + 6 = 90`

`(1 + 1 + 1)n + 6 = 90`

`3n + 6 = 90`

`3n + 6 - color(red)(6) = 90 - color(red)(6)`

`3n + 0 = 84`

`3n = 84`

`(3n)/color(red)(3) = 84/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 28`

`n = 28`

The smallest of the three numbers is 28

Answer 2

The smallest number is 28

Explanation:

Let n = the smallest number
Let n+2 = the second consecutive number
Let n+4 = the third consecutive number

So the equation will be

`n + n+2 + n + 4 = 90` Combining like terms gives.

`3n + 6 = 90` subtract 6 from both sides

`3n + 6 -6= 90 -6-6` This gives

`3n =84` divide both sides by 3

`(3n)/3 = 84/3` This gives

`n =28`

Answer 3

The smallest of the three consecutive even numbers with a sum of 90 is 28.

Explanation:

We should first put this word problem into an algebraic equation to make it easier to solve.

Let `n` be the lowest of the three consecutive even numbers.

We know that our three consecutive even numbers must therefore be `color(red)(n)`, `color(red)(n + 2)`, and `color(red)(n + 4)`. We also know what their sum should be.

`color(red)(n) + color(red)(n + 2) + color(red)(n + 4) = color(green)(90)`

Now, we can solve for `n` as usual.

`3n + 6 = 90`

`3n = 84`

`color(blue)(n = 28)`

And double-checking with this as our lowest of the three consecutive even-numbers:

`color(blue)(28) + color(blue)(28) color(red)(+ 2)+ color(blue)(28) color(red)( + 4)`

`= color(green)(90)`