Algebra 4\
Algebra Problem Week 5
Joby Weatherwax
Introduction to Algebra (MAT 221)
Stacie Williams
Apr 14, 2013
Algebra Problem Week 5
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?
The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared.
A^2+b^2=C^2
We know that Ahmed has a map with a distance to the treasure of 2x+6.
We know that Vanessa has a map with a distance of 2x+4, after walking x paces north.
We are looking to solve for the number of paces north Vanessa must walk.
(number of paces north)^2+ (Vanessa’s distance)^2=(Ahmed’s distance)^2
Substituting known variables
x^2 +(2x+4)^2 =(2x+6)^2
Squaring the known variables
x^2 +(2x+4)(2x+4)= +(2x+6)(2x+6)
Multiplying out the compound equation
x^2 +(4x^2+8x+8x+16)= (4x^2+12x+12x+36)
x^2 +(4x^2+16x+16)= (4x^2+24x+36)
x^2+(4x^2-4x^2)+(16x-24x)+(16-36)=(4x^2-4x^2)+(24x-24x)+(36-36)
Now we have a quadratic equation to solve by factoring and using the zero factor.
x^2-8x-20=0
(x – ) (x + ) = 0
Since the coefficient of x2 is 1 we can start with a pair of parenthesis with an x in each. Since the 20 is negative we know there will be one + and one – in the binomials. We need two factors of -20 which add up to -8. -1, 20; -2, 10; -4, 5; -5, 4; -10, 2; -20, 1
-10 and 2 will work
(x – 10)(x + 2) = 0 Use the zero factor property to solve each binomial, x – 10 = 0 or x + 2 = 0 creating a compound equation. x = 10 or x =
Joby Weatherwax
Introduction to Algebra (MAT 221)
Stacie Williams
Apr 14, 2013
Algebra Problem Week 5
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?
The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared.
A^2+b^2=C^2
We know that Ahmed has a map with a distance to the treasure of 2x+6.
We know that Vanessa has a map with a distance of 2x+4, after walking x paces north.
We are looking to solve for the number of paces north Vanessa must walk.
(number of paces north)^2+ (Vanessa’s distance)^2=(Ahmed’s distance)^2
Substituting known variables
x^2 +(2x+4)^2 =(2x+6)^2
Squaring the known variables
x^2 +(2x+4)(2x+4)= +(2x+6)(2x+6)
Multiplying out the compound equation
x^2 +(4x^2+8x+8x+16)= (4x^2+12x+12x+36)
x^2 +(4x^2+16x+16)= (4x^2+24x+36)
x^2+(4x^2-4x^2)+(16x-24x)+(16-36)=(4x^2-4x^2)+(24x-24x)+(36-36)
Now we have a quadratic equation to solve by factoring and using the zero factor.
x^2-8x-20=0
(x – ) (x + ) = 0
Since the coefficient of x2 is 1 we can start with a pair of parenthesis with an x in each. Since the 20 is negative we know there will be one + and one – in the binomials. We need two factors of -20 which add up to -8. -1, 20; -2, 10; -4, 5; -5, 4; -10, 2; -20, 1
-10 and 2 will work
(x – 10)(x + 2) = 0 Use the zero factor property to solve each binomial, x – 10 = 0 or x + 2 = 0 creating a compound equation. x = 10 or x =
References: Dugopolski, M. (2012). Elementary & Intermediate Algebra. New York: McGraw-Hill.