The sum of two consecutive integers is −13. What are the numbers?

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The sum of two consecutive integers is −13. What are the numbers?

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Answer 1 · 2016-05-05T10:07:44

$- 7 - 6 = - 13$ $-7-6=-13$

Explanation:

$There are other ways of solving this but I have opted to demonstrate a$ $color(blue)("There are other ways of solving this but I have opted to demonstrate a")$
$method that can be used for other condition. For example:$ $color(blue)("method that can be used for other condition. For example:")$ $The sum of 3 consecutive odd numbers and the next even number is 71$ $color(blue)("The sum of 3 consecutive odd numbers and the next even number is 71")$

$15, 17, 19 and 20 \to (n) + (n + 2) + (n + 4) + (n + 5) = 71$ $color(brown)(" 15, 17, 19 and 20" -> (n)+(n+2)+(n+4)+(n+5)=71)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the first number be $n$ $n$
Let the second number be $n + 1$ $n+1$

Then $n + n + 1 = - 13$ $" "n+n+1=-13$

$2 n + 1 = - 13$ $2n+1=-13$

Subtract 1 from both sides

$2 n = - 13 - 1 = - 14$ $2n=-13-1=-14$

Divide both sides by 2

$\frac{2}{2} \times n = - \frac{14}{2}$ $2/2xxn=-14/2$

But $\frac{2}{2} = 1$ $2/2=1$

$n = - 7$ $n=-7$

So the second number is $- 7 + 1 = - 6$ $" "-7+1=-6$

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The sum of two consecutive integers is −13. What are the numbers?

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