The sum of 5 consecutive integers is 110. What are the numbers?

4 Answers
Mar 12, 2018

#20,21,22,23,24#

Explanation:

What, in the first place, are consecutive integers?

They are numbers that come one after another with no numerical gaps. Like these:

#4,5,6,7,8# or these #17,18,19,20,21#

We need to find 5 consecutive integers that add up to 110.

Let's call the first integer in the series #N# for #"number"#. The next integer will be #N +1# since it is #"1 greater"# than #N#.

The next integers will be #N + 2#, #N + 3# and #N +4# since they are 2, 3 and 4 greater than #N# respectively.

#N + (N+1) + (N+2)+(N+3)+(N+4) = 110#

Now remove parentheses and add like terms:
#color(blue)N + color(blue)N+1 + color(blue)N+2+color(blue)N+3+color(blue)N+4= 110#
#color(blue)"5N" + 10 = 110#

Now finish simplifying:
#5N + 10 = 110#
#5N = 100#
#N = 20#

Since #N = 20# our 5 consecutive numbers are:
#20,21,22,23,24#

Mar 12, 2018

#20,21,22,23,24#

Explanation:

Let the first number be#" " x#
Other numbers will be #x+1,x+2,x+3,x+4#

#=>(x)+(x+1)+(x+2)+(x+3)+(x+4)=110#

#=>5x+10=110#

#=>5x=110-10#

#=>5x=100#

#=>x=100/5#

#=>x=cancel100^20/cancel5^1#

#x=20#

The numbers are #" "20,21,22,23,24#

Mar 12, 2018

Please see below.

Explanation:

Let #n# be the middle number. Then the others are #n-2#, #n-1#, #n+1#, and #n+2#

The sum is #5n#, so we need

#5n = 110#

#n = 22#

The numbers are #20#, #21#, #22#, #23#, and #24#

Mar 12, 2018

20, 21, 22, 23, 24

Explanation:

#color(brown)("The mean value is such that if you multiply it by the count of all the")##color(brown)("numbers you get the sum of those numbers (added them all up).")#

#color(brown)("Consecutive means the next, then the next, then the next and so on.")#

5 times the mean value (average) gives 110

Let the mean value be represented by #barx# ( as in statistics)

Then #5barx=110#

divide both sides by 5

#barx=110/5=22#

Middle number is #color(red)(22)# with two others each side of it giving a total count of 5.

#color(green)(ubrace(22-2),color(white)("d")ubrace(22-1),color(white)("d")color(red)(22),color(white)("d")ubrace(22+1),color(white)("d")ubrace(22+2))#

#color(white)("dd")20,color(white)("dddd")21,color(white)("ddd")22,color(white)("dd")23,color(white)("ddddd")24 #