Solve Problems Using Systems in Three Variables
-A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A tree takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 13 hours to paint, and 7 hours to fire. If the workshop has 114 hours for prep time, 79 hours for painting, and 108 hours for firing, How many of each can be made?
A) 6 wreaths, 5 trees, 4 sleighs
B) 5 wreaths, 4 trees, 6 sleighs
C) 4 wreaths, 6 trees, 5 sleighs
D) 7 wreaths, 6 trees, 5 sleighs

Question

Quizplus · Accepted Answer

To solve this problem, we set up a system of equations based on the given information. Let $w$, $t$, and $s$ represent the number of wreaths, trees, and sleighs, respectively. The system of equations is:1. $3w + 16t + 4s = 114$ (Prep time)2. $2w + 3t + 13s = 79$ (Painting time)3. $10w + 4t + 7s = 108$ (Firing time)Solving this system of equations yields the solution: $w = 6$, $t = 5$, and $s = 4$, which corresponds to 6 wreaths, 5 trees, and 4 sleighs.