Question

The sum of Angie's age and John's age equals Michael's age. Angie's age is a prime number, but John's age and Michael's age are not prime numbers. The sum of John's age and Michael's age is a prime number, and Angie's age minus John's age is a prime number. One more than half of John's age is a prime number. Angie is the only teenager, and she is older than John. How old are Angie, John, and Michael?

Answer 1

with an explanation please.

Answer 2

We have
a) A + J = M.
b) A is prime, J, M are not.
c) J + M is prime.
d) A - J is prime.
e) J / 2 + 1 is prime.
f) J ≤ 12 < A < 20 (≤ M, by a), g))
g) M is not a teenager.

So
h) A +2 J is prime (by a), c)).

Answer 3

By e), J ∈ {2, 4, 8, 12}.

By b), J ≄ 2. So J ∈ {4, 8, 12}.

If J = 4, then, by a), f), A ∈ {16, 17, 18, 19}. Then by b), A = 17. This violates c).

So J ∈ {8, 12}.

If J = 8, then by b), f), h), A = 13, so M = 21. This is a solution.

If J = 12, then by b), f), h), there is no solution.

So (A, J, M) = (13, 8, 21) is the unique solution.

Answer 4

wow. amazingly, i followed that. thankyou

Answer 5

lol i just looked it up on google... XD im not that smart!!!!

Answer 6

i don't blame you, eventually i would've done the same thing. lol well thanks for saving me the time of searching and understanding it

Answer 7

ya np!!!