Rithvik's Blog GCSE

In a world where paths are determined by equations, you find yourself at the entrance of a labyrinth. The labyrinth is designed as a giant coordinate plane, with the entrance at the origin (0,0). To navigate through, you must follow a path defined by a series of linear equations, each leading to the next until you find the exit. The path is as follows: Start at the origin. Follow the line defined by the equation y=2x+3 until you intersect with the line defined by x=3. At the intersection, turn and follow the line defined by x=3 upwards until you intersect with the line defined by x+6. Once you reach this second intersection, follow the line x+6 to find the exit. Your task is to calculate the coordinates of the exit of the labyrinth.

A long time ago, a pirate hid his treasure on an island and left a cryptic note for its location. The note says: "Ye who seeks my treasure, listen well. The treasure lies buried where the sum of thrice the age of the oldest tree on the island and twice the number of coconut trees equals 276. If the island has four times as many coconut trees as the oldest tree is years old, solve for the age of the oldest tree and the number of coconut trees." Solve for: The age of the oldest tree on the island. The number of coconut trees on the island. Your Task: Formulate algebraic expressions based on the given clues and solve for the two unknowns.