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11 emus and 27 alpacas...The correct answer is below:

Let x be the number of alpacas & y the number of emus. Obviously an emu has 2 legs & an alpaca has 4 and both have one head. Now you can create a set of 2 equations with 2 unknowns & solve simultaneously to get the answer.

Number of legs: 4x + 2y = 100

Number of heads total: x + y = 38

4x + 2y = 100

x + y = 38 ---> multiply this equation by 2 & subtract from 1st equation

4x + 2y = 100

2x + 2y = 76

--------------------

2x = 24

x = 12

Substitute x=12 in one of the original equations to solve for y:

12 + y = 38

y = 38 - 12 = 26

So the farmer has 12 alpacas & 26 emu.

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