Question 778407: Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2w+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 pases 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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2w+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?
:
This is a pythag problem; a^2 + b^2 = c^2
Starting from Castle Rock: a = x; b = (2x+4); c = (2x+6)
Therefore we have
x^2 + (2x+4)^2 = (2x+6)^2
FOIL
x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36
Subtract 4x^2 fro both sides and combine on the left
x^2 + 16x - 24x + 16 - 36 = 0
x^2 - 8x - 20 = 0
Factors to
(x-10)(x+2) = 0
The positive solution
x = 10
:
So we have go 10 paces north, 24 paces east, that point is 26 paces from C.R.
You can check this out using pythag
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