High School

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

Answer :

To solve the word problem, let's break it down step-by-step:

1. Understand the Problem:
- Kayla wants to determine how many invitations she has already mailed out.
- She has invited a total of 20 friends.
- There are 12 invitations left to send.

2. Determine the Relationship:
- The total number of invitations is the number that she has already sent plus the number of invitations still left to send.

3. Translate into an Equation:
- Suppose [tex]\( x \)[/tex] is the number of invitations Kayla has already mailed.
- Then we can say that:
[tex]\[
x + \text{invitations left to send} = \text{total invitations}
\][/tex]
- Substitute the known values into the equation:
[tex]\[
x + 12 = 20
\][/tex]

4. Solve the Equation:
- To find [tex]\( x \)[/tex], subtract 12 from both sides of the equation:
[tex]\[
x + 12 - 12 = 20 - 12
\][/tex]
- Simplifying gives:
[tex]\[
x = 8
\][/tex]

So, Kayla has already mailed 8 invitations.

The correct equation to use from the given options is:
[tex]\[
\boxed{x+12=20}
\][/tex]

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