Question

Question #bc525

Answer 1

Set up an equation using n, n+2, n+4

Explanation:

let n = the first even integer. then
let n+2= the second even integer then
let n+4 = the third even integer so

n + n +

Answer 2

`22, 24, 26`

Explanation:

We can model this with an equation. If we define our first integer as `x`, the second will be `x+2` and the third will be `x+4`. We can combine these terms, set equal to 72, and solve the equation.

First integer `color(blue)(blue)`, second integer `color(red)(red)`, third integer purple (it's not letting me write in purple here)

`color(blue)(x)+color(red)(x+2)+color(purple)(x+4)=72`

Combining like terms, we get:

`3x+6=72`

Subtract 3 from both sides to get:

`3x=66`

Dividing by 3, we get:

`x=22`

Notice, we just arrived at `x=22`, which means 22 is the first number. Now we can just substitute in 22 for x for our expressions:

Integer 2 `(x+2)= 22+2=24`
Integer 3 `(x+4)= 22+4=26`

Therefore, our 3 consecutive even integers are 22, 24 and 26.

Answer 3

Answer: `{22,24,26}`

Explanation:

Find 3 consecutive even integers whose sum is 72

We can begin by setting up an equation that models the problem
Let `x` be some integer (note that `x` is not necessarily even)

Since we want to have 3 consecutive even integers, we can write our middle integral value as `2x` and our left and right values as `2x-2` and `2x+2`, respectively. Note that we must multiply `x` by `2` in order to make sure our value is even. *

Now that we have our 3 consecutive integers, namely `2x-2, 2x, 2x+2`, we can write that their sum is `72`, as given in the problem:
`(2x-2)+(2x)+(2x+2)=72`; the parentheses here are for emphasis purposes only and are not required

Combining like-terms, we have:
`6x+0=72`

Now we can solve for `x` by dividing both sides by `6`:
`x=72/6=12`

But wait! Our consecutive even integers are of the form `2x-2,2x` and `2x+2`. Therefore, we must plug in our solved `x` value into each expression to find our set of integer values:
`2x-2=2(12)-2=22`
`2x=2(12)=24`
`2x+2=2(12)+2)=26`

Therefore, our consecutive even integers are `{22,24,26}`

*Sidenote: we choose the middle term first since we know that the added constant to each side would cancel each other out and thus make the problem less lengthy, this applies especially well to more complex problems that involve a series of consecutive values