A cake for eight people would require 8 / 4 = <<8/4=2>>2 times as many eggs as a 4 people cake.
If a 4-person cake requires 2 eggs, then an 8-person cake requires 2 x 2 = <<2*2=4>>4 eggs.
Tyler needs to buy 4 - 3 = <<4-3=1>>1 more egg.
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