Joel and jacob are brothers. This year both of their ages are prime numbers. Last year both of their ages were composite numbers.Both of their ages will be composite numbers again over the next three years. If joel and jacob are both teenagers, how old are they now?
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The only teen primes are 13 and 17 and 19
17 is no good, since 18,19,20 are not all composite.
So, they are 13 and 19
To determine the ages of Joel and Jacob currently, we will use the given information step by step:
First, we know that this year both of their ages are prime numbers. Since Joel and Jacob are siblings and both teenagers, we can conclude that their ages are between 13 and 19 (inclusive), as these are the only prime numbers in that range.
Next, we are told that last year both of their ages were composite numbers. Composite numbers are positive integers greater than 1 that are divisible by more than just 1 and themselves. Taking this into consideration, we can exclude the prime numbers from the previous range (13, 17, and 19), leaving us with the composite numbers 14, 15, 16, 18.
Given that both of their ages will be composite numbers again in the next three years, we can exclude the prime numbers from the range in the first step as well. Therefore, we only need to consider the composite numbers 14, 15, 16, and 18.
Considering the intersection of the composite numbers from the last two steps, we find that the only number that satisfies all the given criteria is 14. Both Joel and Jacob must be 14 years old.