Question

The sum of three prime numbers is 100 if one of them exceeds another by 36 then one of the numbers is

Answer 1

Hi ,

2 , 31 , 67 are three prime required

numbers .

sum of three primes = 2 + 31 + 67 = 100

and

67 is 36 more than 31 .

I hope this helps you.

: )

Answer 2

Define x:

Let x be the one of the 3 prime numbers

Express the 3 prime numbers in term of x:

Number 1 = x

Number 2 = x + 36

Number 3 = 100 - (x + 36) - x = 64 -2x

Since we know that the sum of the 3 prime numbers is 100.

⇒ Then all the 3 numbers must be smaller than 100.

There are 25 prime numbers that are smaller than 100

⇒ We will use the trial and error method to find a match for x, starting with the smallest prime number, 2 and work its ways up.

And here is the solution:

When x = 31

Number 1 = x  = 31 (prime number checked)

Number 2 = 31 + 36 = 67 (prime number checked)

Number 3 = 64 - 2x = 64 - 62 = 2 (prime number checked)

Add them up:  31 + 67 + 2 = 100 (Sum of 100 checked)

Answer: The 3 numbers are 3, 31 and 67