Question

Three pieces of fruit have an average weight of m grams. After another piece of fruit is added, the average weight doubles. Find the weight of the extra piece of fruit in terms of m.

Answer 1

x1 = weight of the first piece

x2 = weight of the secound piece

x3 = weight of the third piece

x4 = weight of the fourth piece ( extra piece )


Average weight of first three pieces:

( x1 + x2 + x3 ) / 3 = m

Multiply both sides by 3

x1 + x2 + x3 = 3 m


Average weight of four pieces:

( x1 + x2 + x3 + x4 ) / 4 = 2 m

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Remark:

( x1 + x2 + x3 = 3 m )

so:
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( 3 m + x4 ) / 4 = 2 m

Multiply both sides by 4

3 m + x4 = 8 m

Subtract 3 m to both sides

3 m + x4 - 3 m = 8 m - 3 m

x4 = 5 m


The weight of the extra piece = 5 m