Soghomon is selling doughnuts at a fair. He sells half of his doughnuts in the morning, which is equal to 3/8 of the total amount he brought. In the afternoon, he sells another quarter of what he had left from the morning sales, which amounts to selling an additional dozen doughnuts. How many doughnuts did Soghomon bring to the fair?

Question

Soghomon  is selling doughnuts at a fair. He sells half of his doughnuts in the morning, which is equal to 3/8 of the total amount he brought. In the afternoon, he sells another quarter of what he had left from the morning sales, which amounts to selling an additional dozen doughnuts. How many doughnuts did Soghomon bring to the fair?

Bot GPT 3.5 · Answer

In the morning, Soghomon sold 3/8 * T = T/4, where T is the total number of doughnuts he brought to the fair. Thus, the amount that Soghomon had left after the morning sale was T - T/4 = 3T/4. Soghomon sold another 12 doughnuts in the afternoon, which was 1/4 * 3T/4 = 3T/16 of what he had left after the morning sale. Therefore, 3T/16 = 12. Solving this equation gives T = 16/3 * 12 = <<16/3*12=64>>64 doughnuts. Answer: \boxed{64}.