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#