Directions: Solve the following problems, applying the Ancient Chinese solution procedure highlighted in Chapter 8 of the historic Nine Chapters. Construct a system with three equations and three unknowns, assigning variables as x, y, and z; then, transpose with the first or topmost equations coefficients and constant moving from horizontally on top to vertically at the right in column formatting. After performing the appropriate operations, rewrite as a triangular system and back substitute to solve for the variables and answer any secondary questions. A formal algebraic solution is expected for each problem in this exercise, showing all work.

-----> When Jackson, Madison, and Tyler arrived at the conference room for a morning meeting, they realized that each had bought some breakfast items from the same bakery across the street. Jackson purchased three (3) doughnuts and three (3) muffins for $6; Madison bought one (1) bagel and two (2) muffins for $3; and Tyler picked up two (2) bagels and four (4) doughnuts for $4. A colleague, Jefferson, asked how much each item cost. Unfortunately, none of them noticed. Figure out each item's individual price.

-----> A local minor league baseball team sells three kinds of seats to its home games: bleacher seats, reserve seats, and box seats. During a recent three-game homestead, the front office reported the following advance ticket sales for future home games. On the first day, five (5) bleacher seats, three (3) reserve seats, and two (2) box seats were sold, totaling $63; on the second day, three (3) bleacher seats, two (2) reserve seats, and six (6) box seats were sold, totaling $92; and on the third day, four (4) bleacher seats, eight (8) reserve seats, and two (2) box seats were sold, totaling $94. What is the price to buy one (1) pair of (a) box, (b) reserve, and (c) bleacher seats?