The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
The two numbers are 4 and 9.
Explanation
This problem asks us to find two numbers that satisfy two distinct mathematical conditions simultaneously. The first condition is that their product (the result of multiplying them) is 36. The second condition is that their sum (the result of adding them) is 13. We can solve this logically by listing the factors of 36 and checking their sums.
First, let’s identify all the pairs of whole numbers that multiply to give 36. These are called the factor pairs of 36.
- 1 and 36
- 2 and 18
- 3 and 12
- 4 and 9
- 6 and 6
Since the product (36) and the sum (13) are both positive, we know that both of the numbers we are looking for must also be positive. Therefore, we do not need to consider negative factors.
Next, we will test each of these pairs against the second condition: do they add up to 13?
- 1 + 36 = 37. This does not equal 13.
- 2 + 18 = 20. This does not equal 13.
- 3 + 12 = 15. This does not equal 13.
- 4 + 9 = 13. This is the correct sum.
- 6 + 6 = 12. This does not equal 13.
Through this process of elimination, we find that the only pair of numbers that multiplies to 36 and also adds to 13 is 4 and 9.
This type of problem is a fundamental concept in algebra, often used as a first step in factoring quadratic equations. For example, to factor the equation x² + 13x + 36 = 0, you would look for two numbers that multiply to 36 and add to 13, which are precisely 4 and 9.
