The sum of four consecutive odd integers?

The sum of four consecutive odd integers is three more than 5 times the least of the integers.

Update:

I don't get the last part, I get the four consecutive integers, though.

7 Answers

Relevance
  • Anonymous
    1 decade ago
    Best Answer

    Any odd integer can be written as (2n + 1) for some integer n. The 2n is even and adding the one makes it odd.

    ---------------------

    So the four integers are:

    2n + 1

    2n + 3

    2n + 5

    2n + 7..............................and their total is:

    -----------

    8n + 16

    So 8n+ 16 = 3 + 5*(2n + 1)......Expand the right hand side of this equation.

    8n + 16 = 3 + 10n + 5......Subtract 8n from both sides.

    16 = 2n + 8...........Subtract 8 from both sides

    8 = 2n..................Divide both sides by 2

    4 = n

    n = 4

    The integers are ((2*4) + 1) = 9 and then 11, 13, and 15.

    Now to check the answer: 9+11+13+15 = 48

    48 ?= 3 + (5*9)

    48 ?= 3 + 45

    48 ?= 48......Yes it does. So the answers check and are valid.

    Summarizing. The integers are 9, 11, 13, and 15...<<..Answer

  • 1 decade ago

    Let x be the smallest integer. Since they are consecutive odd, there is a difference of two between each one, so the three other integers are x + 2, x + 4, and x + 6. The sum of all of those is three more than 5 times the least. Remember that the least integer is x, so you have 5 times that, which would be 5x, and then 3 more added on to it, which is 5x + 3:

    x + (x + 2) + (x + 4) + (x + 6) = 5x + 3

    4x + 12 = 5x + 3

    12 = x + 3

    9 = x

    ANSWER: The integers are 9, 11, 13, and 15.

  • 1 decade ago

    Least of the integers (x):

    5x + 3 = x + x + 2 + x + 4 + x + 6

    x = 9

    2nd integer:

    = 9 + 2

    = 11

    3rd integer:

    = 9 + 4

    = 13

    4th integer:

    = 9 + 3

    = 15

    Answer: 9, 11, 13 & 15 are the integers.

    Proof (3 is the difference after deducting 5 times the least of integers from the sum of all integers):

    = (9 + 11 + 13 + 15) - 5(9)

    = 48 - 45

    = 3

  • 1 decade ago

    x is the lowest integer, since the integers are odd, they go up by 2 from the lowest number

    x + (x+2) + (x + 4) + (x + 6) = 5x + 3

    Simplify by adding the xs and numbers

    4x + 12= 5x + 3

    Subtract 4x from both sides

    12 = x + 3

    Subtract 3 from both sides

    9 = x

    9 is the lowest integer, and just add two to that each time to get the consecutive odd integers

    the integers are 9, 11, 13, and 15

  • How do you think about the answers? You can sign in to vote the answer.
  • Anonymous
    1 decade ago

    x + (x+2) + (x+4) + (x+6) = 5x +3

    4x +12 = 5x + 3

    9 = x

    so the numbers are: 9, 11, 13, 15 = 48

    5(9) + 3 = 48 checks

  • 1 decade ago

    2n+1 is an odd interger #1

    2n+1+2n+3+2n+5+2n+7=3+5(2n+1)

    8n+16=3+10n+5

    8n+16=10n+8

    8=2n

    4=n

    the numbers are

    2(4)+1=9

    2(4)+3=11

    2(4)+5=13

    2(4)+7=15

  • 3 years ago

    enable x be the 1st type. x+x+2+x+4+x+6=216. 4x+12=216. 4x=204 x=fifty one Numbers are atypical and sequential (or use the algebra i.e x, x+2, x+4 etc), so series is fifty one, fifty 3, fifty 5, fifty seven.

Still have questions? Get your answers by asking now.