The sum of 2 consecutive numbers is 53. [closed]

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The sum of 2 consecutive numbers is 53.

I need to find those numbers, but I'm not even sure how to set up the problem.

Any suggestions?

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2 Answers

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Two consecutive numbers are pairs of numbers like $\,1, 2\,$ or $\,18, 19$: "one right after the other". That is, one of the integers is immediately to the right of the other, when viewed on a number line.

Denote the smaller integer using $n$. Then the larger of the two consecutive integers must be $n+1$. That leaves us with solving the following: $$n + (n+1) = 2n + 1 =53.$$

That means $\;2n = 53-1 = 52,\;$ so $\;n =\dfrac {52}2 = 26$.

So, we have $\;n = 26, \;n+1 = 27,$ as desired.

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$$x+(x+1)=53 \iff 2x+1=53 \iff 2x=52 \iff x=26$$

The numbers are:

$x=26$ and $x+1=27$

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