Question 211667: Ahmed has first half of 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 go to the 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’?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Obviously, the 2 halves of the map must indicate that the treasure is in the same location
With Ahmed’s instructions that the treasure is (2x + 6) paces from Castle Rock, a diagram would indicate that the distance from Castle Rock, which is at a southern point, to the treasure spot, would form the hypotenuse of a right triangle - a hypotenuse that goes from south to the north-east (I wish I could draw the diagram to make it much clearer).
Based on Vanessa’s half, the “x” paces from Castle Hill, in a northern direction, and the (2x + 4) paces in an eastern direction, would form the legs of the right triangle.
Therefore, we would have a right triangle that would have legs of “x” and “(2x + 4),” and a hypotenuse of (2x + 6) paces. Using the Pythagorean formula, we will then have:
(x – 10)(x + 2) = 0
So, x – 10 = 0, or x + 2 = 0 -------> x = 10, or – 2 (ignore as measurement CANNOT be negative)
Therefore, 
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