Select the correct answer.

The product of two numbers is 21. If the first number is -3, which equation represents this situation and what is the second number?

A. The equation that represents this situation is [tex]x - 3 = 21[/tex]. The second number is 24.
B. The equation that represents this situation is [tex]3x = 21[/tex]. The second number is 7.
C. The equation that represents this situation is [tex]-3x = 21[/tex]. The second number is -7.
D. The equation that represents this situation is [tex]-3 + x = 21[/tex]. The second number is 18.



Answer :

Let's break down the given information and find the correct equation and second number step-by-step.

We are given:
- The product of two numbers is 21.
- The first number is -3.

We need to identify the correct equation and find the second number.

1. Identify the correct equation:
- The product of two numbers means we multiply the first number by the second number to get 21.
- Let the second number be [tex]\( x \)[/tex].
- Since the first number is -3, our equation becomes:

[tex]\[ -3 \cdot x = 21 \][/tex]

Reviewing the options:
- Option A: [tex]\( x - 3 = 21 \)[/tex] (This is incorrect because it represents a different operation, subtraction, rather than multiplication).
- Option B: [tex]\( 3x = 21 \)[/tex] (This is incorrect because the first number should be -3, not 3).
- Option C: [tex]\( -3x = 21 \)[/tex] (This is the correct equation as it correctly represents the multiplication of -3 and [tex]\( x \)[/tex] yielding 21).
- Option D: [tex]\( -3 + x = 21 \)[/tex] (This is incorrect because it represents an addition operation, rather than multiplication).

Therefore, the correct equation is [tex]\( -3x = 21 \)[/tex].

2. Solve for the second number:
- We solve the equation [tex]\( -3x = 21 \)[/tex] for [tex]\( x \)[/tex].

[tex]\[ -3x = 21 \][/tex]

[tex]\[ x = \frac{21}{-3} \][/tex]

[tex]\[ x = -7 \][/tex]

So, the second number is [tex]\( -7 \)[/tex].

Thus, the correct answer is:

C. The equation that represents this situation is [tex]\( -3x = 21 \)[/tex]. The second number is -7.