Answer:
A
Step-by-step explanation:
Let the smallest number be n.
If the next integer differs by 3 then:
n + 3 is our second integer.
If the product is 108 then we would multiply them together.
n * (n + 3) = 108 Now solve for n.
(n*n) + (n*3) = 108
[tex]n^{2} +3n = 108[/tex] Now we move 108 to the other side by subtracting so we can factor.
[tex]n^{2} + 3n - 108 = 0[/tex]
(n )(n ) = 0
Find all the multiples of 108
1 x 108
2 x 54
3 x 36
4 x 27
6 x 18
9 x 12
Which one can we add or subtract together to get 3?
9 x 12 because 12 - 9 = 3
[tex]n^{2} + 3n - 108 = 0[/tex]
(n 12)(n 9) = 0 Now we figure out the signs. Since we have -108 one must be negative, and the 3 in the 2nd term (3n) is positive so:
(n + 12)(n - 9) = 0 Is our factored equation.
Our smallest number is 9, so n = 9
Our second number is n + 3 and 9 + 3 = 12
So our 2 integers are 9, 12, there sum would be 9 + 12 = 21
Option A.
