SOLUTION: 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 i

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): You can put this solution on YOUR website!
2x+6=x+2x+4
2x+6=3x+4
2=x
or x=2
2(2)+6=2+2(2)+4
24=24
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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