Final answer:
Only statements b and c are correct, as they correctly represent the other number in terms of x and identify one of the numbers in the solution set of the sum and product equations given.
Step-by-step explanation:
The question involves solving a system of equations represented by the sum and product of two numbers. The sum of two numbers is 22, and their product is -48. Let's establish the equations:
We can rearrange the sum equation (x + y = 22) to express y in terms of x, which gives us y = 22 - x. This corresponds to statement b.
Next, we use the product equation to find the actual values of x and y. Since the product of the two numbers is negative, one of them must be negative and the other positive.
- y = 22 - x
- x(22 - x) = -48
This expands and rearranges to the quadratic equation:
Solving the quadratic equation, we get x = -2 or x = 24. If x = -2, then y = 22 - (-2) = 24. If x = 24, then y = 22 - 24 = -2. Therefore, the numbers -2 and 24 satisfy both conditions.
From the choices given:
- The other number can be represented by (22 - x), which matches statement b.
- One of the numbers is indeed -2, which matches statement c.
Statement a, d, and e are incorrect, and statement c is partly correct but could also refer to the correct number +24.
To summarize, only statements b and c are correct.