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­If 2w + y = 47, 3y + z = 112, and 2w + 3z = 21, what is the average of w, y, and z?

A. 15
B. 25
C. 50
D. 100
E. It cannot be determined from the information given.

Solution

Multiply eq 1. by -3  we will get

-3(2w + y = 47) ---> -6w - 3y = -141 then adding eq. 1 & 2 we will get

-6w - 3y = -141
  z  + 3y =  112
--------------------
-6w + z  = -29 -----> eq. 4
 
Then multiply 3 eq. by 3 we will get

3(2w + 3z = 21) ----> 6w + 9z = 63 then adding eq. 3 & 4 we will get

6w + 9z = 63
-6w + z  = -29
------------------
z        = 3.4

As we know the value of z so, we can find the values of w = 5.4 and y = 36.2
Now, we can find the average of w, y, and z using the formula sum of all observations/no. of observation we will get 15 as the answer

Option A is correct

 
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