Question

The average of three numbers is 52.If the first two numbers average is 47.5 and last two numbers average is 55.5 then find the second number

Answer 1

Answer:

second number value is 50, first value 45 and third value 61

Answer 2

Answer:  The required second number is 50.

Step-by-step explanation:  Given that the average of three numbers is 52,  the first two number's average is 47.5 and last two number's average is 55.5.

We are to find the second number.

Let x, y and z represents the given three numbers.

Then, according to the given information, we have

$\dfrac{x+y+z}{3}=52\\\\\Rightarrow x+y+z=156~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

$\dfrac{x+y}{2}=47.5\\\\\Rightarrow x+y=95~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$\dfrac{y+z}{2}=55.5\\\\\Rightarrow y+z=111~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Adding equations (ii) and (iii), we have

$(x+y)+(y+z)=95+111\\\\\Rightrarow x+2y+z=206~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

Subtracting equation (i) from equation (iv), we get

$(x+2y+z)-(x+y+z)=206-156\\\\\Rightarrow y=50.$

Thus, the required second number is 50.