Solve using a system of three linear equations.
-A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 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, 16 hours to paint, and 7 hours to fire. If the workshop has 109 hours for
Prep time, 81 hours for painting, and 122 hours for firing, How many of each can be made?
A)3 wreaths, 9 trees, 5 sleighs
B)9 wreaths, 5 trees, 3 sleighs
C)5 wreaths, 3 trees, 9 sleighs
D)10 wreaths, 6 trees, 4 sleighs

Question

Quizplus · Accepted Answer

To solve this, we set up a system of equations based on the given information:1. For preparation time: $3W + 14T + 4S = 109$2. For painting time: $2W + 3T + 16S = 81$3. For firing time: $9W + 4T + 7S = 122$Where $W$ is the number of wreaths, $T$ is the number of trees, and $S$ is the number of sleighs.Solving this system of equations, we find that $W = 9$, $T = 5$, and $S = 3$, which corresponds to option B: 9 wreaths, 5 trees, 3 sleighs.

Solve Using a System of Three Linear Equations