# 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.

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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

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

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

w = 100  -81 = 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

Sources:

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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.