Question

the sum of three prime number is 101.the difference of two of them is 24.what are the number? ​

Answer 1

Hey❤️

Since the sum is odd, all of the primes are odd.

There aren't to many primes under 100, so just find two that differ by 24 by looking at the odd primes plus 24. When you find a pair, subtract the sum from 101 to see if it's prime.

3 + 24 = 27, not prime

5 + 24 = 29, prime. 101 - 29 - 5 = 67, prime. So 5, 29, 67 is a solution.

There may be more.

7 + 24 = 31, 101 - 38 = 63, not prime

11+ 24 = 35

13 + 24 = 37, 101 - 50 = 51, not prime

17 + 24 = 41, 101 - 58 = 43, another prime, so 17, 41, 43 is another solution. (I've corrected the mistake I had here earlier.)

19 + 24 = 43, 101 - 62 = 39, not prime

23 + 24 = 47, 101 - 66 = 35, not prime.

...You should check the rest yourself to make see whether there are any more solutions.