Solve the problem.
-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, 14 hours to paint, and 7 hours to fire. If the
Workshop has 101 hours for prep time, 55 hours for painting, and 82 hours for firing, how many of each can be
Made?
A)2 serving bowls, 6 platters, 5 bread baskets
B)7 serving bowls, 6 platters, 3 bread baskets
C)6 serving bowls, 5 platters, 2 bread baskets
D)5 serving bowls, 2 platters, 6 bread baskets

Question

Quizplus · Accepted Answer

We can create a system of equations based on the time needed for each type of product:

3x + 15y + 4z = 101 (prep time)
2x + 3y + 14z = 55 (painting time)
8x + 4y + 7z = 82 (firing time)

Solving this system of equations using matrix operations or substitution will give us x = 6, y = 5, and z = 2. This means we can make 6 serving bowls, 5 platters, and 2 bread baskets. Therefore, the best choice is C.

Solve the Problem. -A Ceramics Workshop Makes Serving Bowls, Platters, and Bread Baskets