Kate is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $27 for the meal, plus $3 per pound for the lobster she picks. At the second restaurant, Kate would pay $4 per pound for the lobster, in addition to $25 for the meal. Kate realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Kate pay for her dinner? What is the weight?