Question

There are 4 successive whole numbers that sum to -66. What are these numbers?

Answer 1

Let the consecutive integers be
`n, n+1, n+2 and n+3`

Given condition is
`n+( n+1)+ (n+2)+( n+3)=-66`
`=>4n=-66-1-2-3`
`=>4n=-72`
`=>n=-72/4=-18`

Consecutive integers are
`-18, -18+1, -18+2 and -18+3`
`-18, -17, -16 and -15`

Answer 2

There is a trick to this type of question.

`-15-16-17-18= -66`

Explanation:

Notice that we have negative 66 so I elect to count increasingly negative.

Let a value be `n`

So we have: `" "(n)+(n-1)+(n-2)+(n-3)=-66`

`4n-6=-66`

`4n=-60`

`n=-60/4=-15`

Check: `-15-16-17-18= -66`
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`color(blue)("Would this work if I counted in the direction towards positive. ")`

That is; becoming les negative

`(n)+(n+1)+(n+2)+(n+3)=-66`

`4n+6=-66`

`4n=-72`

`n=-18`

`(-18)+(-18+1)+(-18+2)+(-18+3)`

`-18-17-16-15`