Write a system of linear equations in three variables, and then use matrices to solve the system.
-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 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 100 hours for firing, how many of each can be made?
A) 7 wreaths; 4 trees; 2 sleighs
B) 4 wreaths; 2 trees; 7 sleighs
C) 2 wreaths; 7 trees; 4 sleighs
D) 8 wreaths; 5 trees; 3 sleighs

Question

Quizplus · Accepted Answer

The system of linear equations based on the given information is:$$ \begin{align*}3w + 14t + 4s &= 85 \quad \text{(Prep time)} \2w + 3t + 15s &= 56 \quad \text{(Painting time)} \10w + 4t + 7s &= 100 \quad \text{(Firing time)}\end{align*} $$Solving this system using matrices (or any other method) yields the solution: 7 wreaths (w), 4 trees (t), and 2 sleighs (s).

Write a System of Linear Equations in Three Variables, and Then