Question

What are are two consecutive integers, such that seven times the larger minus three times the smaller is 95?

Answer 1

The numbers are `22` and `23`

Explanation:

Alright, to solve a problem like this, we need to read and define as we go. Let me explain.

So we know that there are two consecutive integers. They can be `x` and `x+1`. Since their consecutive, one has to be `1` number higher (or lower) than the other.

Ok, so first we need "seven times the larger"

`7(x+1)`

Next, we need to "minus three times the smaller"

`7(x+1)-3x`

Is equal to "`95`"

`7(x+1)-3x=95`

Alright! There's the equation, now we just need to solve for `x`! First we are going to get everything on one side and distribute the `7`.

`=7x+7-3x-95`

`=4x-88`

Pull out a `4`

`=4(x-22)`

Now that we have two terms, we can set them both equal to `0` and solve.

`4!=0`

This can never be true, lets move to the next term

`(x-22)=0`

`x=22`

That's it! So your two consecutive numbers are `22` and `23`!

If you want to check this, just put `22` in place of the `x` and `23` in place of the `(x+1)` in the equation we made above!

Hope this helps!
~Chandler Dowd