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<p>According to the problem, half of the cakes were made with 4 eggs each. Two-thirds of “the rest” is two-thirds of “one half” or one third. Therefore we can say one third of the cakes were made with three eggs each, and the remaining 54 cakes were made with two eggs each.</p>
<p>Since 1/2 + 1/3 + 1/6 = 1, we can say that 54 cakes comprise 1/6 of the total number of cakes. Therefore 1/2 and 1/3 of the total number are 162 and 108 cakes, respectively, and we can say that</p>
<p>162 cakes were made with 4 eggs each
108 cakes were made with 3 eggs each
54 cakes were made with 2 eggs each</p>
<p>The total number of eggs used is 162(4) + 108(3) + 54(2) = 1080.</p>