Question

If the Arithmetic means of the 17 numbers is 14. when the two numbers are eliminated the mean becomes 13 if the differences of the two eliminated numbers is 7. find the numbers.

Answer=30,20 but show me in process.​

Answer 1

The numbers are 18 and 25

Explanation:

Given

`\bar x_1 = 14`
`n_1 = 17`

`\bar x_2 = 13`
`n_2 = 15`

`a - b = 7` --- the difference of the 2 numbers

Required

Find a and b

We have:

`\bar x = (\sum x)/(n)` -- mean formula

So, we have:

`\bar x_1 = (\sum x_1)/(n_1)`

`14 = (\sum x_1)/(17)`

Cross multiply

`\sum x_1 = 14 * 17`

`\sum x_1 = 238`

When the two numbers are removed, we have:

`\bar x_2 = (\sum x_2)/(n_2)`

`13 = (\sum x_2)/(15)`

Cross multiply

`\sum x_2 = 13 * 15`

`\sum x_2 = 195`

The two numbers that were removed are:

`a + b = \sum x_1 - \sum x_2`

`a + b = 238 - 195`

`a + b = 43`

Make a the subject

`a= 43 - b`

We have:

`a - b = 7`

Substitute
`a= 43 - b`

`43 - b - b = 7`

`43 - 2b = 7`

Collect like terms

`2b = 43 - 7`

`2b = 36`

Divide by 2

`b = 18`

Substitute
`b = 18` in
`a= 43 - b`

`a = 43 - 18`

`a = 25`