Answer to Problem of the Month for 9/2017

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 =

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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

September 2017 Problem of the Month

Correctly solved by:

September 2017
Problem of the Month