SOLUTION: Help find the treasure.....please... Is this (2x+6)=2x+4/x or 1/2x+6+2x+4=1 Ahmed has first half of a treasure map, which indicates that the treasure is buried in the dese

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Question 60821This question is from textbook Elementry and Intermediate Algebra
: Help find the treasure.....please...
Is this (2x+6)=2x+4/x
or 1/2x+6+2x+4=1

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’? This question is from textbook Elementry and Intermediate Algebra

Found 2 solutions by hayek, solver91311:
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
Vanessa's portion tells us: "walk ‘x’ paces to the North, and then walk (2x + 4) paces to the East [from castle rock]" suggests a right-triangle with sides x and (2x+4). So the distance from castle rock that you would walk if you went straight to the treasure is given by the pythagorean theorem:
sqrt%28%282x%2B4%29%5E2%2Bx%5E2%29
Ahmed's portion says the distance from castle rock that you would walk if you went straight there is:
2x%2B6
So, set those two equal to each other and solve for x:
sqrt%28%282x%2B4%29%5E2%2Bx%5E2%29=2x%2B6%29
Square both sides:
%282x%2B4%29%5E2%2Bx%5E2=%282x%2B6%29%5E2
4x%5E2%2B16x%2B16%2Bx%5E2=4x%5E2%2B24x%2B36
x%5E2-8x-20=0
%28x-10%29%28x%2B2%29=0
Assuming x must be positive (otherwise the treasure map is quite misleading), the answer is:
highlight%28x=10%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


And in what world should a treasure map NOT be misleading? If you use the negative root, then instead of going +2 paces North, you go -2 paces North, in other words, 2 paces South. Then you go 2(-2) + 4 = 0 paces East. And looky there, you are 2(-2) + 6 = 2 paces from castle rock, as Ahmed's part of the map advertised. Note that Ahmed's part of the map said NOTHING about direction, so his value doesn't have to come out negative to be correct. With the information given, you may have to dig in two different places to find the treasure.

John

My calculator said it, I believe it, that settles it
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