Can you determine the ages of Mr. P's Grandchildren from the 7 clues below?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Give the age for each of the following grandchildren:
|
|
Ben = |
|
|
Carrie = |
|
|
Elizabeth = |
|
|
Jackson = |
|
|
James = |
|
|
Kate = |
|
|
Stewart = |
Click here for a printer version of this puzzle
Solution to the Problem:
Ben = 11
Carrie = 17
Elizabeth = 2
Jackson = 13
James = 19
Kate = 13
Stewart = 7
To solve the puzzle, let B= Ben's age, C = Carrie, E = Elizabeth,
X = Jackson, J = James, K = Kate, and S = Stewart.
Then you can write the following seven equations:
(1) X + K = J + S
(2) J = E + C
(3) B + C = K + X + E
(4) B + E = X
(5) J + K = 32
(6) B + K = S + 17
(7) B + S + C = J + K + E + 1
Then C - E = K + E (eq #3 - eq #4)
So, C - K = 32
K = 32 - J (eq #5)
Then K = 32 - J
C - (32 - J) = 2E
C + J - 2E = 32
-C + J - E = 0
So, 2J - 3E = 32
Sub eq #4 in eq #1: (B + E) + K = J + S
E + S + C = J + S>br>
Then J - E = 17
So, 2J - 3E = 32
J - E = 17
-3J + 3E = -51
So, J = 19 and K = 13
Now substitute the values for J and K in the original equations:
(1) X = S + 6
(2) E + C = 19
(3) B + C = X + E + 13
(4) B + E = X
(5) 32 = 32
(6) B = S + 4
C = 19 - E (eq #2)
C = 2E + 13 (eq #3 - eq #4)
3E = 6, so E = 2 and then C = 17
B = S + 4 (eq #1 + eq#3)
B + S = J - 1 (eq #7)
B - S = 4
B + S = 18
2B = 22, so B = 11. Then S = 7 and X = 13.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Brijesh Dave | Mumbai City, Maharashtra, India |
| 3. McKenzie Martin |
Mountain View High School, Mountain View, Wyoming |
| 4. Bob Currie |
R E Campbell Company, Houston, Texas |
| 5. Lorenzo | Quezon City, Phillipines |
| 6. Joe Curtis | Armona, California |
| 7. Alyssa Rippetoe |
Mountain View High School, Mountain View, Wyoming |
| 8. Kaylee Gross |
Mountain View High School, Mountain View, Wyoming |
| 9. Alexis Saxton |
Mountain View High School, Mountain View, Wyoming |
| 10. Mikaela Williams |
Mountain View High School, Mountain View, Wyoming |