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If the sum of a prime number and a composite number is 15 and the product is 36, what are the two numbers
Method 1: let one of the numbers be x and the other be 15-x
Then: X (15-x) = 36
-x²+15x-36=0
The solution is X1 = 12, X2 = 3
3 is prime, 12 is composite, 3 + 12 = 15
So these two numbers are 3 and 12, respectively
Method 2: the sum of two numbers = 15 is: 1 and 14, 2 and 13, 3 and 12, 4 and 11, 5 and 10, 6 and 9, 7 and 8,
Where two numbers multiply by 36 only: 3 and 12, where 3 is prime and 12 is composite
Method 3: decompose 36 into 2 × 2 × 3 × 3
One of them is prime and the other is composite: 2 and 2 × 3 × 3 = 18,3 and 2 × 2 × 3 = 12
The sum of two numbers = 15 is only satisfied by 3 and 12
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