Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours toprepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4hours to fire. A sleigh takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has113 hours for preparation time, 64 hours for painting, and 101 hours for firing, how many of each can bemade?
A)7 wreaths, 6 trees, 2 sleighs
B)6 wreaths, 2 trees, 7 sleighs
C)2 wreaths, 7 trees, 6 sleighs
D)8 wreaths, 7 trees, 3 sleighs

Question

Quizplus · Accepted Answer

To determine how many of each item can be made, we need to find out how many of each item can be made based on the amount of time available for each process. 
For preparation, we have 113 hours available. A wreath takes 3 hours to prepare, so we can make 113/3 = 37.6 wreaths. A tree takes 14 hours to prepare, so we can make 113/14 = 8 trees. A sleigh takes 4 hours to prepare, so we can make 113/4 = 28.25 sleighs. However, we cannot make fractional items, so to maximize the number of items made, we should round down to the nearest whole number.
For painting, we have 64 hours available. A wreath takes 2 hours to paint, so we can make 64/2 = 32 wreaths. A tree takes 3 hours to paint, so we can make 64/3 = 21.33 trees. A sleigh takes 16 hours to paint, so we can make 64/16 = 4 sleighs. Again, we round down to the nearest whole number.
For firing, we have 101 hours available. A wreath takes 9 hours to fire, so we can make 101/9 = 11.22 wreaths. A tree takes 4 hours to fire, so we can make 101/4 = 25.25 trees. A sleigh takes 7 hours to fire, so we can make 101/7 = 14.43 sleighs. Once again, we round down to the nearest whole number.
Therefore, the maximum number of each item that can be made is 7 wreaths, 6 trees, and 2 sleighs. Thus, the best choice is A)7 wreaths, 6 trees, 2 sleighs. To solve the problem, we can set up a system of equations:

3w + 14t + 4s = 113 (hours for preparation)
2w + 3t + 16s = 64 (hours for painting)
9w + 4t + 7s = 101 (hours for firing)

where w = number of wreaths made, t = number of trees made, and s = number of sleighs made.

Solving the system of equations, we get:

w = 7
t = 6
s = 2

Therefore, the workshop can make 7 wreaths, 6 trees, and 2 sleighs. Choice A is the correct answer.

Write the Word or Phrase That Best Completes Each Statement