This is a hands-on activity in which students will solve systems of three equations with three unknowns using matrices specifically RREF and Cramers rule. Students are given a sealed, opaque bag containing three different types of candies and the total quantity of candies the bag contains. Students are also given access to candies not in their bag to obtain an average weight of an individual candy. They then weigh the bag with the candy and an empty bag to obtain the weight of the total candies their bag contains. A "hint" is written on the outside of the bag such as "there are three times more musketeers than kisses." Students then create three equations 1. x + y + z = total quantity 2. weight(x) + weight (y) + weight (z) = total weight 3. Equation based on the hint given.
Students then use matrices and RRE and Cramers Rule to solve for each variable. Open the bag in the teacher's presence to verify their results and then eat the candies as a reward!

Similar activites are avaiable with substitution & elimination in two and three variables. Students love this activity and it was a hit at the UCTM conference. Have fun!