Castle Rock
Castle Rock
Donna K. Martin
MAT221: Introduction to Algebra
11/18/2013
Instructor: Vallory Shearer
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 is a Pythagorean problem a²+b²=c²
Let a=x and b=2x+4 so c=2x+6
If I just know Ahmed’s half, the treasure has to be at the outer edge of a circle with center at Castle Rock and radius = 2x+6 paces. Vanessa’s half says “walk x paces to the north, and then walk 2x+4 paces to the east.” But her instructions must put her on the edge of Ahmed’s circle with radius = 2x+6
The radius and the North and South walk’s from a right triangle, so
(2x+6) ² = x² + (2x+4)² The binomial into the Phythagorean
4x²+24x+36=x²+4x²+16x+16 The binomials squared, there is a 4x², Subtract 4x² from both sides of the equation
24x+36=x²+16x+16 Subtract 24x from both sides of the equation
36=x²-8x+16 Subtract 36 from both sides x²-8x-20 = 0 This is called a Quadratic equation to solve by factoring and using the zero factor.
Now solve for x
(x- ) (x+ ) Since the coefficient of x² is 1, I can start with a pair of parenthesis with an x in each. Since 20 is negative we know that there will be one + and 1 negative in the binomials
(x-10)*(x+2) =0 Use the zero factor property to solve each binomial, x- 10 = 0 0r x+ 2 = 0 creating a compound equation x = 10 or x = -2 Possible solution to or equation
We have something called an extraneous solution, which mean that it doesn’t work with the scenario. A negative pace or negative distance in a measured geometric figure, so -2 solution does not work, an d it leaves us with x=10 x=10 ANSWER
Now
Donna K. Martin
MAT221: Introduction to Algebra
11/18/2013
Instructor: Vallory Shearer
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 is a Pythagorean problem a²+b²=c²
Let a=x and b=2x+4 so c=2x+6
If I just know Ahmed’s half, the treasure has to be at the outer edge of a circle with center at Castle Rock and radius = 2x+6 paces. Vanessa’s half says “walk x paces to the north, and then walk 2x+4 paces to the east.” But her instructions must put her on the edge of Ahmed’s circle with radius = 2x+6
The radius and the North and South walk’s from a right triangle, so
(2x+6) ² = x² + (2x+4)² The binomial into the Phythagorean
4x²+24x+36=x²+4x²+16x+16 The binomials squared, there is a 4x², Subtract 4x² from both sides of the equation
24x+36=x²+16x+16 Subtract 24x from both sides of the equation
36=x²-8x+16 Subtract 36 from both sides x²-8x-20 = 0 This is called a Quadratic equation to solve by factoring and using the zero factor.
Now solve for x
(x- ) (x+ ) Since the coefficient of x² is 1, I can start with a pair of parenthesis with an x in each. Since 20 is negative we know that there will be one + and 1 negative in the binomials
(x-10)*(x+2) =0 Use the zero factor property to solve each binomial, x- 10 = 0 0r x+ 2 = 0 creating a compound equation x = 10 or x = -2 Possible solution to or equation
We have something called an extraneous solution, which mean that it doesn’t work with the scenario. A negative pace or negative distance in a measured geometric figure, so -2 solution does not work, an d it leaves us with x=10 x=10 ANSWER
Now