Solve Problems Using Systems in Three Variables
-A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A platter takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has 92 hours for prep time, 60 hours for painting, and 94 hours for firing, how many of each can be made?
A) 8 serving bowls, 4 platters, 2 bread baskets
B) 4 serving bowls, 2 platters, 8 bread baskets
C) 2 serving bowls, 8 platters, 4 bread baskets
D) 9 serving bowls, 5 platters, 3 bread baskets

Question

Quizplus · Accepted Answer

To solve this problem, we set up a system of equations based on the given information:1. For preparation time: $3b + 15p + 4k = 92$2. For painting time: $2b + 3p + 16k = 60$3. For firing time: $8b + 4p + 7k = 94$Where $b$ represents the number of serving bowls, $p$ represents the number of platters, and $k$ represents the number of bread baskets. Solving this system of equations yields the solution: 8 serving bowls, 4 platters, and 2 bread baskets.