Answer:
y = [tex]\frac{1}{5}(x^{2}-35x)[/tex]
Step-by-step explanation:
Let the total numbers are n.
If the average of y numbers is x then we can form an equation
[tex]\frac{y}{n}=x[/tex]
⇒ [tex]\frac{n}{y}=\frac{1}{x}[/tex]
⇒ n = [tex]\frac{y}{x}[/tex] --------(1)
Now 30 is added to the set of numbers then average becomes (x - 5)
[tex]\frac{y+30}{n+1}=(x-5)[/tex]
⇒ [tex]\frac{(n+1)}{(y+30)}=\frac{1}{(x-5)}[/tex]
⇒ (n + 1) = [tex]\frac{y+30}{x-5}[/tex]
⇒ n = [tex]\frac{y+30}{x-5}[/tex] - 1 ----- (2)
Now we equate the values of n from equation 1 and 2
[tex]\frac{y}{x}[/tex] = [tex]\frac{y+30}{x-5}[/tex] - 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 = [tex]\frac{1}{5}(x^{2}-35x)[/tex]
