Final answer:
To find the product of the two numbers, we need to solve the system of equations formed by the given information. The two numbers are 3 and -27, and their product is -81.
Step-by-step explanation:
To find the product of the two numbers, we need to solve the system of equations formed by the given information. Let's assume the first number is x and the second number is y.
From the first sentence, we have x - y = 30.
From the second sentence, we have (2/3)x + (1/11)y = 5.
To solve this system of equations, we can use the method of substitution or elimination. Let's use elimination:
Multiplying the second equation by 11 gives us (22/33)x + (1/11)y = 55/11.
Multiplying the first equation by 33 gives us 33x - 33y = 990.
Adding these two equations eliminates the y variable:
55/33x = 55/11 + 990.
Simplifying gives us 55/33x = 605/11.
Multiplying both sides by (33/55) gives us x = 605/11 * 33/55.
Simplifying further gives us x = 33/11 = 3.
Substituting this value back into the first equation gives us 3 - y = 30.
Simplifying gives us y = -27.
Therefore, the two numbers are 3 and -27, and their product is -81.