Question

The average of 3, 7, 8 and x is 5 and the average of 2, 19, 7, x and y is 10. what is the value of y?

Answer 1

$Average= \frac{Sum}{total no.}$

Let's consider the first average in the question
Let's add the terms

3+7+8+x
Sum=18+x
We have found sum. Now for the total no.
Count the terms
There are four terms
Total no.=4

Average=5...............(given)

THUS in the formula

$Average= \frac{sum}{total no.}$

Substitute the values

$5= \frac{18+x}{4}$

Cross multiply

$20=18+x$

Shift 18 to RHS

$20-18=x$

$x=2$

Now considering the second average

Sum=2+19+7+x+y
       =28+(2)+y.................(substituting the value of x)
Sum=30+y
Lets count the terms we added
They are five terms

Total no.=5

Average=10.............given

$Average= \frac{sum}{total no.}$

$10= \frac{30+y}{5}$

$50=30+y$

$50-30=y$

$y=20$

ANS: The value of y is 20