Answer to October 2016 Problem of the Month

Farmer Smith and his wife have fifteen children born at intervals of one year and a half.

Pocahontas, the oldest child, admits that she is eight times as old as Captain John, the youngest of the brood.

How old is Pocahontas?

Show your work using algebra.
Let p = age of Pocahontas and j = age of Captain John.

Solution to the Problem:

Pocahontas is 24 years old.

p = 8 j
p = j + (14 x 1.5) since there are 13 kids in between them.

So solve the two equations:
p = 8j
p = j + 21

Substituting for p in the second equation, 8j = j + 21, so 7j = 21 and j = 3.
Then p = 8(3) = 24.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Kimberly Howe	Vienna, Virginia
3. Britan Woody	Mountain View High School, Mountain View, Wyoming
4. Eliza Sheffield	Tuscaloosa, Alabama
5. Chase Smith	Mountain View High School, Mountain View, Wyoming
6. Mashayla Hurdsman	Mountain View High School, Mountain View, Wyoming
7. Alyx Wells	Mountain View High School, Mountain View, Wyoming
8. Rosemary Walker	Mountain View High School, Mountain View, Wyoming
9. Dawson Case	Mountain View High School, Mountain View, Wyoming
10. Hunter Gross	Mountain View High School, Mountain View, Wyoming
11. Brijesh Dave	Mumbai city, Maharashtra, India