Rutgers/Lucent ALLIES IN TEACHING MATHEMATICS AND TECHNOLOGY Grant
Using technology not simply to do things better, but to do better things.


OTHER STUDENT RESPONSES:
The Great One


Answer #1: The individual's age is 84.

Explanation: I started by putting x to equal the age when died. it gave me a paragraph to work with. 1/6 lasted as the youth's life. I took that and got 1/6(x). He grew a beard after 1/12. I took that and got 1/12 (x). After 1/7, he married. I now got 1/7(x). He had a son 5 years later. His son lived 1/2 as long as his father. 1/2(x). He died 4 years later. I have this now too work with.

1/6(x)+1/12(x)+1/7(x)+5+1/2(x)+4=x

I had to find a common dinominator. 84 is what all the numbers go into. Now I have this to work with.

14(x)+7(x)+12(x)+420+42(X)336+84x
Add common terms.
75x+756=84x
-75x       -75x
756=9x
756/9x 9x/9x
84=x.
This is how i Got 84 for the age.

BONUS: octivgerian


Answer #2: The Great One is 75.6 years old.

Explanation: a = life of the great one.

I converted the fractions to 84ths to make it easier.

14/84 + 7/84 + 12/84 + 5 = the time the son was born. Because the son is half as old as his father when he died and died four years before the father. So:

32/84 + 9 = 42/84(or 1/2a)

subtract 32/84 from both sides

9 = 10/84a
9 = 5/42a
9 = 1/8.4a

multiply both sides by 8.4
75.6 = 1a

so the Great One was 75.6


Answer#3: The great one is 10 years old.

Explanation: I cahnged all the fractions so they had a common denominator. I came up with 84 as a common denominator. I added 14/84 to 7/84 to 12/84 to 420/84 to 336/84 and came up with 831/84, so I took 831 divided by 84 and got 96/7 and rounded it to 10 years old.


Answer #4: I think that the Great One was about 32 years old when he died.

Explanation: 1/6 + 1/12 + 1/7 + 5 + 4 =
1/6 + 1/12 + 1/7 + 9 =
2/12 + 1/12 + 1/7 + 9 =
3/12 + 1/7 + 9 =
1/4 + 1/7 + 9 =
7/28 + 4/28 + 9 =
11/28 + 9/1 =
11/28 + 882/28 = 893/28
893/28 = 31.89
I rounded it off to 32


Answer #5: He lived about 14.8 years.

Explanation: Let 2x= his lifespan

Let x = his son's lifespan

1/6(2x)+1/12(2x)+1/7(2x)+5+4=2x
1/3x+1/6x+2/7x+9=2x
1/2x+2/7x+9=2x
7/14x+4/14x=2x-9
11/14x-2x=-9
-17/14x=-9
x= about 7.4
2x= 14.8 years


Answer#6: The Great One was 61 1/3 years old.

Explanation: To figure out the problem, I used x= the great one's life.

First I added calculated the Great One's life before his son was born:
1/6x + 1/12x + 1/7x + 5.

The one sixth was his youth, the one twelth was the beard he grew, the one seventh the time he was married, and the 5 being the years he was married until he had his son.

Adding up the above figures, I know that:
11/28x + 5 = the Great One's son's life, or half of the the Great One's life, because we know that the Great One's son lived half as long as his father. The original problem tells us that the Great One died four years after his son's death, therefore:
11/28x + 5 = 1/2(x-4)

Then I simplified the equation, solving for x:
11/28x + 5 = 1/2x - 2,
-3/28x = -7,
x = 7(28/3)
x = 61 1/3.

Thus, the Great One is 61 1/3 years old.

BONUS: the special word used to describe people who live to their 6th decade is a sesuagenarian.


Answer#7: The Great Ones Age is 108 years.

Explanation: Wrote out this equation:
1/6 g + 1/12g+1/7g+5+1/2g+4=g
Solve for g by multiplying by 84 the LCM to get rid of the denominators.
Collect like terms:
77g + 756=84g
Solve for g by subtracting 77g from both sides:
756=7g
Solve for g by dividing both sides by 7:
g=108


Answer#8: THe solution to the problem is 8 years.

Explanation: I looked at the end of the problem where it says that HIs son lived half as long as he did and he lived 4 years after his son died. Which means that he must have lived 2(4) years old which=8


Answer#9: He was 39 and his son was 19.5

Explanation: When you calculate all the things that they give you you will figure out his age. you add 1/6 plus 1/12 plus 1/7 plus 5 plus 4 and add that together and get 39. It says that his son was exactly half the age as he was and half his age is 19.5.


Answer#10: The great ones age was 120.

Explanation: We looked up on the internet, and it says that the first 20yrs of your life is your youth. So if his youth was 1/6 of his life, we timesd it by 6, and we got 120!!



Return to Agenda
THE MATH FORUM: Creating community, developing resources, constructing knowledge...