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There are two ways to do it, with or without algebra:
Without algebra:
There are 114 animals.  If they were all ostriches there would have been
only 114×2 or 228 legs.  So there are 314-228 or 86 extra legs which are
possessed by the donkeys, 2 per donkey so there are 86/2 = 43 donkeys and
114-43 or 71 ostriches.
With algebra:
x = the number of donkeys
y = the number of ostriches
1x + 1y = 114    <-- the "heads" equation  
4x + 2y = 314    <-- the "legs" equation:
 Solve by substitution or elimination and get x=43 and y=71.
Edwin
Solve by substitution or elimination and get x=43 and y=71.
Edwin