The sum of 5 consecutive integers is 1,000. What are the numbers?

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Answer 1 · 2017-01-07T19:51:13

The numbers are: 198, 199, 200, 201 and 202

If we let the smallest of the five consecutive integers be $x$ ,

then the other 4 consecutive integers, by definition of "consecutive" would be:

$x + 1$ , $x + 2$ , $x + 3$ and $x + 4$

These five integers equal 1,000 so we can write:

$x + x + 1 + x + 2 + x + 3 + x + 4 = 1000$

We can now solve for $x$ :

$5x + 10 = 1000$

$5x + 10 - color(red)(10) = 1000 - color(red)(10)$

$5x + 0 = 990$

$5x = 990$

$(5x)/color(red)(5) = 990/color(red)(5)$

$(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 198$

$x = 198$

Then:

$x + 1 = 199$

$x + 2 = 200$

$x + 3 = 201$

$x + 4 = 202$