Christopher has a stick that he has marked out in tenths. He has to break the stick into three pieces of which no two pieces can have the same length. Give three equations that show different ways in which he could break the stick.
Let x be the length of the first piece, y be the length of the second piece, and z be the length of the third piece.
1) x + y + z = 10
This equation states that the sum of the lengths of all three pieces should be equal to the total length of the stick, which is 10 units.
2) x ≤ y ≤ z
This equation indicates that the lengths of the pieces should be arranged in increasing order, ensuring that no two pieces have the same length.
3) x < 4, y > 4, z > 6
This equation ensures that the first piece has a length less than 4, the second piece has a length greater than 4, and the third piece has a length greater than 6. This guarantees that all three pieces have different lengths.
These equations together represent different ways in which Christopher could break the stick into three pieces without any two pieces having the same length.