Final answer:
Using a system of equations, we determine the two numbers with a ratio of 9:11 and difference of 6 to be 27 and 33, making the correct answer (c) 27, 33.
Step-by-step explanation:
To find two numbers where their ratio is 9:11 and their difference is 6, we can use algebra to set up a system of equations based on the information given. Let's denote the two numbers as x and y, with x being the smaller number.
We have two conditions:
- The ratio of the numbers is 9:11, which can be expressed as x/y = 9/11.
- The difference between the numbers is 6, expressed as y - x = 6.
From the first condition, we can say that x = 9k and y = 11k for some constant k. Using the second condition, we substitute these expressions into y - x = 6 to get 11k - 9k = 6.
Solving this, we find that 2k = 6 and thus k = 3. Substituting back in, we find that x = 9(3) = 27 and y = 11(3) = 33. Therefore, the two numbers are 27 and 33.
The correct answer from the multiple choice options given is (c) 27, 33.