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

2 Answers
A08
Mar 6, 2017

Let the consecutive integers be
n,n+1,n+2andn+3

Given condition is
n+(n+1)+(n+2)+(n+3)=−66
⇒4n=−66−1−2−3
⇒4n=−72
⇒n=−724=−18

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

Tony B
Mar 6, 2017

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=−604=−15

Check: −15−16−17−18=−66
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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

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