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All Names Are Fictitious
Thanks
Ark
Answer:
Noah and Emzara are
thirty-six years old.
Ham,
Japheth and
Shem are triplets.
They
are six years
old
AI answer
Let's denote the ages as follows:
- Noah's age = N
- Emzara's age = E
- Ham's age = H
- Japheth's age = J
- Shem's age = S
Now, let's use the clues to form equations:
1. Noah and Emzara are the parents: (N = E)
2. The three children are Ham, Japheth, and Shem: (H, J, S)
3. Multiply Ham and Japheth's ages to obtain Noah's age: (H times J = N)
4. Multiply Japheth and Shem's ages to obtain Emzara's age: (J times S = E)
5. Add all five people to obtain 90: (N + E + H + J + S = 90)
6. The difference between Noah and Emzara's ages is the same as the
difference between the ages of Ham and Japheth: (|N - E| = |H - J|)
7. The difference between Noah and Emzara's ages is the same as the
difference between the ages of Japheth and Shem: (N - E = J - S)
Now, let's solve these equations:
From 1, we know (N = E).
From 3 and 4, we know (H times J = N) and (J times S = E).
Substitute the values of N and E from equation 1:
[H times J = E]
[J times S = E]
This implies (H times J = J times S).
Since each child has a different age, we can conclude that (H = S).
Now, substitute (N = E) and (H = S) into equation 6:
[|N - E| = |H - J|]
[|N - N| = |H - J|]
[0 = |H - J|]
This means that (H = J).
Now, let's go back to equation 5:
[N + E + H + J + S = 90]
Substitute (N = E), (H = S), and (H = J):
[E + E + S + J + S = 90]
[2E + 2S + J = 90]
Now, let's use the fact that each child is 6 years old ((H = J = S = 6)):
[2E + 2(6) + 6 = 90]
[2E + 18 = 90]
[2E = 72]
[E = 36]
Now that we know Emzara's age ((E = 36)), we can find Noah's age ((N = E = 36)).
And since each child is 6 years old, the ages are as follows:
- Noah's age = 36
- Emzara's age = 36
- Ham's age = 6
- Japheth's age = 6
- Shem's age = 6
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