Question

The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x − 5. What is the value of y in terms of x ?

Answer 1

Answer: y = x/5 - 7

Explanation:

Please see the workings attached .

Answer 2

y =
`(1)/(5)(x^(2)-35x)`

Explanation:

Let the total numbers are n.

If the average of y numbers is x then we can form an equation

`(y)/(n)=x`

⇒
`(n)/(y)=(1)/(x)`

⇒ n =
`(y)/(x)` --------(1)

Now 30 is added to the set of numbers then average becomes (x - 5)

`(y+30)/(n+1)=(x-5)`

⇒
`((n+1))/((y+30))=(1)/((x-5))`

⇒ (n + 1) =
`(y+30)/(x-5)`

⇒ n =
`(y+30)/(x-5)` - 1 ----- (2)

Now we equate the values of n from equation 1 and 2

`(y)/(x)` =
`(y+30)/(x-5)` - 1

y(x - 5) = x(y + 30) - x(x - 5) [ By cross multiplication ]

xy - 5y = xy + 30x - x² + 5x

xy - xy - 5y = 35x - x²

-5y = 35x - x²

x² - 35x = 5y

y =
`(1)/(5)(x^(2)-35x)`