Given that a and b are prime numbers such that 3a + 7b= 209, determine the value of a + b.
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1 Answer

a=(209-7b)/3. When b=2, a=65, when b=5, a=58, when b=11, a=44, etc.,

The pattern is: b=2+3n, a=65-7m where m and n are positive integers.

We can tabulate these values:

a   b

65 2

58 5

44 11

30 17

16 23

2   29

Note that apart from the number 2 for b, all even values for b have been omitted, because they are all divisible by 2, so are not prime. b=5+6k where k is a positive integer.

The only pair of primes is a=2 and b=29.

by Top Rated User (1.2m points)

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