Please help me solve this problem: Ahmed has half a treasure map, which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. ...
Please help me solve this problem:
Ahmed has half a treasure map, which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?
Thank you.
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
Ahmed has half a treasure map, which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east.
The two decide to share the information available in their maps. They get to Castle Rock, and walk x paces to the north and then 2x + 4 paces to the east. This position is 2x + 6 paces from Castle Rock. Using the Pythagorean Theorem gives:
x^2 + (2x + 4)^2 = (2x + 6)^2
=> x^2 + 4x^2 + 16 + 16x = 4x^2 + 36 + 24x
=> x^2 = 20 + 8x
=> x^2 - 8x - 20 = 0
=> x^2 - 10x + 2x - 10 = 0
=> x(x - 10) + 2(x - 10) = 0
=> (x + 2)(x - 10) = 0
=> x = -2 and x = 10
Ignoring the negative solution of the equation, x = -2, we get x = 10
The value of x determined from the information provided by both their maps is 10.