Question

The sum of two numbers is 22 and their product is -48. Let x = one of the numbers. Identify all the

statements below that are correct.
a. The other number can be represented by (x - 22)
b. The other number can be represented by (22-x)
c. One of the numbers is -24
c. One of the numbers is -2
d. The other number can be represented by (-46 - x)
e. One of the numbers is -12

Answer 1

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:

• x + y = 22
• xy = -48

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:

• x2 - 22x - 48 = 0

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.