Final answer:
The two numbers that meet the conditions of adding up to -72 and multiplying to -27 are 9 and -81. This is derived by finding pairs of factors of -27 and determining which pair also sums up to -72.
Step-by-step explanation:
The question asks to find two numbers that add up to -72 and multiply to -27. We can approach this problem by setting up a system of equations based on the given conditions. Let's designate the numbers as x and y. Thus, we have:
- x + y = -72 (sum of the numbers)
- xy = -27 (product of the numbers)
We can use the multiplication rules for signs to understand these equations better. When two numbers multiply to a negative number (-27), one of them must be positive, and the other must be negative. Based on the rules of addition, when we add a positive number and a negative number, we subtract the smaller number from the larger number, and the resulting sign will be that of the larger number in absolute value.
Since we know their product and sum, an effective method to find the two numbers is to use factoring. The product xy = -27 suggests that we are looking for factors of -27. Possible pairs of factors that multiply to -27 include (3, -9), (-3, 9), (1, -27), and (-1, 27).
To determine which pair also adds to -72, we check the sum of each pair. The pair that adds up to -72 is (9, -81), since 9 + (-81) = -72 and 9 * (-81) = -729.
The two numbers that add up to -72 and multiply to -27 are 9 and -81.