MAT 221 Introduction to Algebra
Instructor Alicia Davis
September 29, 2013
Treasure hunts have always been a big deal in our home. Having raised five boys, anything to do with an adventure was exciting. Actually, this past June I planned one of my grandsons birthday parties around the theme of pirates and treasure hunting. I had never considered the math that went behind the maps in which I made up. Needless to say, when I saw the question entitled “buried treasure” in our math book, it brought back numerous memories.
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 ...view middle of the document...
So if I put these measurements into the Pythagorean Theorem than I have the following:
(2x +6) = x + (2x +4) The original equation.
(2x + 6)2 = x2 + (2x + 4)2 The binominals into the Pythagorean Theorem.
(2x + 6)(2x + 6) = x2 + 4x2 +16x + 16
4x2 + 24x + 36 = 5x2 + 16x + 16 Combined all like terms.
-4x2 – 24x – 36 Subtract from both sides of the equation.
0 = x2 – 8x – 20 This is the quadratic equation to solve by factoring and
Using the zero factor.
(x + 2) (x – 10) = 0 The coefficient of x2 is one. Since both the 24 and the 36
are negative I know that there must be one negative and
one positive. I need two factors of negative 20 which add
up to negative 8.
The factors used were positive 2 and negative 10.
x + 2 = 0 I used the zero factor property to solve each binomial.
x – 10 = 0 This creates a compound equation.
x = -2. 10 These are the two possible solutions to the original
The final equation is what is referred to as extraneous, because it can not be used when
discussing paces. Since it is not possible to have negative paces, then it is reasonable to
determine that x = 10 paces. In a measured geometric figure -2 does not work, thus x = 10 is the
key. The treasure lies 10 paces north and 2x + 4 = 2(10) + 4 = 24 paces east of Castle Rock or
2x + 6 = 2(10) + 6 = 26 paces straight from the rock.
Given the fact that the normal age group that is interested in “treasure hunting” in my family
starts around the age of 4, and usually ends around the age of 12, I would have to say that I
should continue to make my maps more simplistically than having the “pirates” solve for x or
use the Pythagorean Theorem. However, as a final assignment for this class, this certainly made
for an interesting equation to solve!
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: