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 + 8 = 12[/tex]

B. [tex]x + 20 = 12[/tex]

C. [tex]x + 12 = 20[/tex]

D. [tex]x - 8 = 20[/tex]

Sure! Let's go through the word problem step by step to find which equation we need to solve:

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?

Step-by-Step Solution:

1. Define the total number of invitations Kayla needs to send:
- Kayla wants to send invitations to 20 friends.

2. Determine how many invitations are left to be sent:
- There are 12 invitations left to send out.

3. Find the number of invitations that have already been sent:
- Let [tex]$ x $[/tex] represent the number of invitations Kayla has already sent.

4. Set up an equation:
- If there are 12 invitations left to send and the total number of invitations is 20, we can write the equation as:
[tex]\[ \text{(invitations sent)} + \text{(invitations left to send)} = \text{(total invitations)} \][/tex]
- Substituting the known values:
[tex]\[ x + 12 = 20 \][/tex]

So, the correct equation needed to solve the problem is:
[tex]\[ x + 12 = 20 \][/tex]

Therefore, the correct choice is C. [tex]$ x + 12 = 20 $[/tex].