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