3) A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas.

Question

3) A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 85 hours for prep time, 56 hours for painting, and 86 hours for firing, How many of each can be made? A) 2 wreaths, 7 trees, 4 sleighs C) 7 wreaths 4 trees, 2 sleighs B) 8 wreaths, 5 trees, 3 sleighs D) 4 wreaths, 2 trees, 7 sleighs

Explanation / Answer

Setup this sytem of equations

3*W + 14*T + 4*S = 85 (for total prep time)

2*W + 3*T + 15*S = 56 (total paint time)

8*W + 4*T + 7*S = 86 ( and for total firing time)

Solving above three equations would yield: (Use Cramer's rule or whatever method you are aware)

W = 7

T = 4

S = 2

Thus option C is corrrect: 7 wreath, 4 trees , 2 sleigh

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