From the seven clues below, can you determine how old Mr. P's Grandchildren will be or would have been in 2026?
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Give the age for each of the following grandchildren:
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Ben = |
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Carrie = |
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Jackson = |
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James = |
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Kate = |
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Libby = |
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Stewart = |
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Solution to the Problem:
Here is the solution:|
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Ben = 20 |
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Carrie = 26 |
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Jackson = 22 |
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James = 28 |
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Kate = 22 |
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Libby = 11 |
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Stewart = 16 |
Let X = age of James
Let J = age of Jackson
Let B = age of Ben
Let C = age of Carrie
Let S = age of Stewart
Let L = age of Libby
Let K = age of Kate
We solve the system:
1. K=J
2. J=2L
3. X+C+K+J+B+S+L=145
4. K+B+L+1=X+C
5. B+S+1=C+L
6. X−L=S+1
7. K+C=3S
Step 1: Use the simple substitutions
From (1) and (2):
K=J=2L
Step 2: Rewrite everything in terms of L
From (6):
X=S+1+L
From (7):
C=3S−2L
From (5):
B=4(S−L)
Solving the reduced system gives:
L=11
Step 3: Find all remaining variables
S=(3L−1)/2=16
B=2L−2=20
C=26
X=28
K=22
J=22
Correctly solved by:
| 1. Elizabeth Pleacher | Bastrop, Texas, USA |
| 2. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 3. Diana Kennett | Bastrop, Texas, USA |
| 4. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
| 5. Max Long |
Central High School, Grand Junction, Colorado, USA |
| 6. Johanna Villeda |
Central High School, Grand Junction, Colorado, USA |
| 7. Davit Banana | Istanbul, Turkey |
| 8. Ivy Joseph | Pune, Maharashtra, India |
| 9. Ryleigh Regan |
Central High School, Grand Junction, Colorado, USA |
| 10. Dakoda Perrigo |
Central High School, Grand Junction, Colorado, USA |
| 11. Kelly Stubblefield | Mobile, Alabama, USA |