The numbers x , y , z and w have an average equal to 25. The average of x , y and z is equal to 27. Find w.

Expert Answers
changchengliang eNotes educator| Certified Educator

Total (x, y, z, w) = 25 * 4 = 100

Total (x, y, z) = 27 *3 = 81

w = 100  -81 = 19

The required answer, w=19

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A note:

The gist of questions on average is to be versatile in converting from average to total and vice versa, at all times being very mindful of how many numbers (or elements) we are dealing with at each stage.

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Some formulae:

Average = Total / number of elements

Total = Average x number of elements

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To have a more thorough definition of average and total, click on the links provided below

 

hala718 eNotes educator| Certified Educator

Given that the average of (x , y, z and w ) = 25

Then we know that the average = sum of all numbers/ total of numbers

==> Ave = (x + y + z+w)/4 = 25

==> multiply by 4:

==> x + y + z + w = 100...........(1)

 

Also , given the average of x , y and z is 27

==> Ave = (x+ y+ z) /3 = 27

Multiply by 3:

==> (x+ y+ z) = 81 ............(2)

We will substitute (2) in (1):

==> (x + y + z ) + w = 100

==> 81  + w = 100

Now subtract 81 from both sides:

==> w = 100 - 81

==> w = 19

neela | Student

The average of x, y,z and w  is 25.

Therefore  the verage of  x,y,z and w  =  (x+y+z+w)/4 = 25.

Multiplying by 4 we get:

So x+y+z+w = 25*4

 x+y+z+w = 100....(1).

The verage of x,y and z = 27.

Therefore Average of x,y and z = (x+y+z)/3 = 27.

Multiply by 3:

Therefore  x+y+z = 27*3 = 81.

x+y+z = 81....(2)

Eq (1) - eq (2) gives:

x+y+z+w - (x++y+z) = 100-81.

x+y+z+w-x-y-z =  19

w = 19.

Therefore z = 19.

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