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OlgaM077 [116]
3 years ago
7

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 t

he value of y in terms of x ?

Mathematics
2 answers:
Alenkasestr [34]3 years ago
6 0

Answer:

y = \frac{1}{5}(x^{2}-35x)

Step-by-step explanation:

Let the total numbers are n.

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

\frac{y}{n}=x

⇒ \frac{n}{y}=\frac{1}{x}

⇒ n = \frac{y}{x} --------(1)

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

\frac{y+30}{n+1}=(x-5)

⇒ \frac{(n+1)}{(y+30)}=\frac{1}{(x-5)}

⇒ (n + 1) = \frac{y+30}{x-5}

⇒ n = \frac{y+30}{x-5} - 1 ----- (2)

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

\frac{y}{x} = \frac{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 = \frac{1}{5}(x^{2}-35x)

aleksley [76]3 years ago
6 0

Answer: y = x/5 - 7

Step-by-step explanation:

Please see the workings attached .

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