Question

the average of three cosective integer such that twice the greatest integer is 2 less than times the least integer

Answer 1

@I_Need_Help_With_Home

Answer 2

@waterineyes

Answer 3

Let the three consecutive numbers be : \((x-1)\), \(x\), \((x+1)\)

Answer 4

ok

Answer 5

Average of three numbers is given by:
\[Average = \frac{\tt {Sum \ of \ three \ numbers}}{\tt{Number \ of \ Numbers}}\]

Answer 6

right

Answer 7

As you have three numbers, so their sum would be:
\(Sum = x-1 + x + x+1\) implies \(Sum = 3x\)

Answer 8

And as you have three numbers, so number of numbers are \(3\).

Answer 9

And you have also one relation given in question, we try to use that.
out of that three numbers, \((x+1)\) would be greatest of all, and \((x-1)\) will be smallest number.

Answer 10

And the relation is:
\(2(x+1) = 2(x-1) + 2\)

Answer 11

Sorry:
\(2(x+1) = 2(x-1) - 2\)

Answer 12

Can you find out \(x\) from here?

Answer 13

yes

Answer 14

Then find out \(x\), and tell me.

Answer 15

less than 3 times the least integer ??

Answer 16

@waterineyes the average of three cosective integer such that twice the greatest integer is 2 less than3 times the least integer

Answer 17

3?

Answer 18

Then it would be:

\(2(x+1) = 3(x-1)-2\)

Answer 19

Can you find \(x\) here now?

Answer 20

@rosebird doing?

Answer 21

tag me when you are done. :)

Answer 22

yeh

Answer 23

why 3 befor bracket??

Answer 24

why u put 3 before bracket? @waterineyes

Answer 25

7? is answer :) ty @waterineyes

Answer 26

3 times the least integer means 3 multiplied by least integer and least integer is \((x-1)\).
So, \(3 \times (x-1)\)

Answer 27

\(x =7\), but it is \(x\) value.

Now we have to find Average.

Answer 28

but the answers are
6
7
8

Answer 29

I already calculated above that sum is \(3x\) and number of numbers you have is \(3\):
So:
\[Average = \frac{Sum}{Total number} = \frac{3x}{3} \implies \color{green}{Average = x}\]

Answer 30

It is your luck that value of \(x\) is average itself. :P

Answer 31

hahaha thanks:) @waterineyes

Answer 32

Do you want to know how \(x\) is average itself?