sum of four consecutive integers is - 42

Question

Consecutive numbers. Finding a negative number

 

Answer 1

Here's a different approach to finding the numbers. Because they are consecutive we can use arithmetic.

Find the average of the four numbers.

-42/4=-10.5

Two consecutive integers whose average is -10.5 are -10 and -11. What about the other two consecutive integers ?

They both can't be less than -11 and they both can't be greater than -10. However, one can be less than -11 and one can be greater than -10. They are consecutive so therefore the other two numbers are -12 (less than -11) and

-9 (greater than -10).

-12, -11, -10, and -9 are the consecutive integers

Now you have two different ways to solve a problem like this, algebra and an equation and arithmetic and average.

Answer 2

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

 

n + (n+1) + (n+2) + (n+3) = -42

 

Combining like terms:

 

4n + 6 = -42

4n = -48

 

n = -12

 

The four integers are (-12, -11, -10, -9).  Check:

 

-12 + (-11) + (-10) + (-9) = -42

-12 - 11 - 10 - 9 = -42

-42 = -42   Check!