CAN ANYONE PLEASE HELP? 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 17 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 119 hours for prep time, 87 hours for painting, and 108 hours for firing, how many of each can be made?

Question

luffingsails · Answer

It's setting up a system of equations.

There is 119 hours for prep, 87 hours to paint, and 108 hours for firing. So just collect all of the information for each object and step.

Let x = number of wreaths, y = number of trees, and z = number of sleighs.

So, 

3x + 17y + 4z = 119 (the number of hours for prep)
2x + 3y+15z = 87 (number to paint)
10x+4y+7z = 108 (number to fire)

Now just solve the system of equations to determine x, y, and z. Does that help?