College

Select the equation needed to solve the following word problem:

Kayla is sending invitations to 20 of her friends for a pizza party. If there are 12 invitations left to send out, how many invitations has she already mailed?

A. [tex]x + 12 = 20[/tex]
B. [tex]x + 20 = 12[/tex]
C. [tex]x - 8 = 20[/tex]
D. [tex]x + 8 = 12[/tex]

Answer :

To solve the problem of how many invitations Kayla has already mailed, we can set up an equation using the information given in the word problem.

1. Understand the given information:
- Kayla is sending invitations to a total of 20 of her friends.
- There are 12 invitations left to send out.

2. Identify what we need to find:
- We need to find out how many invitations Kayla has already mailed. Let's call this number [tex]\(x\)[/tex].

3. Set up the equation:
- The total number of invitations is the sum of the invitations already mailed ([tex]\(x\)[/tex]) and the invitations left to send out (12). Therefore, we have the equation:
[tex]\[ x + 12 = 20 \][/tex]

4. Select the correct equation from the options provided:
- Option A: [tex]\(x+12=20\)[/tex]
- Option B: [tex]\(x+20=12\)[/tex]
- Option C: [tex]\(x-8=20\)[/tex]
- Option D: [tex]\(x+8=12\)[/tex]

The correct equation that represents the situation is:
[tex]\[ x + 12 = 20 \][/tex]

5. Solve the equation:
- To find [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation:
[tex]\[ x + 12 = 20 \][/tex]
[tex]\[ x = 20 - 12 \][/tex]
[tex]\[ x = 8 \][/tex]

Therefore, Kayla has already mailed 8 invitations.

So, the correct answer is option A: [tex]\(x + 12 = 20\)[/tex].

In conclusion, using this equation, we determined that Kayla has already mailed 8 invitations.