Question 153673This question is from textbook elementary and intermediate algebra
: I'm, stuck can you help? #80. Buried Treasure. Ahmed has 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 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 question is from textbook elementary and intermediate algebra
Answer by stanbon(75887)   (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 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?
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To see the problem draw an x/y coordinate system.
Put Castle Rock (CR) at the intersection of the x and y axis.
Mark a point "x" up the vertical axis from CR.
From that point mark a point 2x+4 to the right.
Use Pythagoras to find the distance that point is from CR:
d = sqrt(x^2 + (2x+4)^2) = sqrt(5x^2+16x+16)
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That point is also 2x+6 from CR according to Ahmed's map.
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EQUATION:
sqrt(5x^2 + 16x + 16) = 2x+6
5x^2 + 16x + 16 = 4x^2+ 24x + 36
x^2 - 8x -20 = 0
(x-10)(x+2) = 0
Positive solution:
x = 10
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Cheers,
Stan H.
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