Answer
All possible answers:
31
17
Work Step by Step
$7k+3 \lt 50$
$7k \lt 47$
$k \lt 6 r 5$
Therefore, we are looking for a positive integer k that is 6 or below. Therefore, the possible values of k are 6, 5, 4, 3, 2, and 1.
Let's try k = 6:
$7k+3 = 7(6)+3 = 45$
Since 45 is not a prime number less than 50, let's try k=5.
Let's try k = 5:
$7k+3 = 7(5)+3 = 38$
Since 38 is not a prime number less than 50, let's try k=4.
Let's try k = 4:
$7k+3 = 7(4)+3 = 31$
*Since 31 is a prime number less than 50, it is a possible answer.*
Since we have found a possible answer, we can stop there. However, to see other possible answers, let's try k = 2 and k = 1.
If k = 2:
$7k+3 = 7(2)+3 = 17$
Since 17 is also a prime number less than 50, it is a possible answer.
If k = 1:
$7k+3 = 7(1)+3 = 10$
10 is not a prime number less than 50.
So, 31 and 17 are two possible answers for this question.
