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Answer :
Let's solve the word problem step-by-step:
1. Understand the problem:
- Kayla is sending invitations to 20 friends in total.
- There are 12 invitations left to be sent out.
- We need to find out how many invitations have already been mailed. Let's denote the number of invitations already mailed by [tex]\( x \)[/tex].
2. Formulating the equation:
- The total number of invitations sent out (which is [tex]\( x \)[/tex] plus the invitations left to send out) equals the total invitations Kayla planned to send (20).
- This can be written as: [tex]\( x \)[/tex] (invitations already mailed) + 12 (invitations left to send) = 20 (total invitations).
3. Writing the equation:
- The correct equation representing this situation is:
[tex]\[
x + 12 = 20
\][/tex]
4. Checking the options:
- Option A: [tex]\( x - 8 = 20 \)[/tex] (Incorrect, as it does not match our formulated equation)
- Option B: [tex]\( x + 20 = 12 \)[/tex] (Incorrect, as it reverses the roles of total and remaining invitations)
- Option C: [tex]\( x + 12 = 20 \)[/tex] (Correct, aligns with our formulation)
- Option D: [tex]\( x + 8 = 12 \)[/tex] (Incorrect, does not match our formulated equation)
5. Conclusion:
- The correct equation needed to solve the word problem is:
[tex]\[
x + 12 = 20
\][/tex]
6. Result identification:
- According to the option list, this equation corresponds to option C.
Hence, the correct option is C.
1. Understand the problem:
- Kayla is sending invitations to 20 friends in total.
- There are 12 invitations left to be sent out.
- We need to find out how many invitations have already been mailed. Let's denote the number of invitations already mailed by [tex]\( x \)[/tex].
2. Formulating the equation:
- The total number of invitations sent out (which is [tex]\( x \)[/tex] plus the invitations left to send out) equals the total invitations Kayla planned to send (20).
- This can be written as: [tex]\( x \)[/tex] (invitations already mailed) + 12 (invitations left to send) = 20 (total invitations).
3. Writing the equation:
- The correct equation representing this situation is:
[tex]\[
x + 12 = 20
\][/tex]
4. Checking the options:
- Option A: [tex]\( x - 8 = 20 \)[/tex] (Incorrect, as it does not match our formulated equation)
- Option B: [tex]\( x + 20 = 12 \)[/tex] (Incorrect, as it reverses the roles of total and remaining invitations)
- Option C: [tex]\( x + 12 = 20 \)[/tex] (Correct, aligns with our formulation)
- Option D: [tex]\( x + 8 = 12 \)[/tex] (Incorrect, does not match our formulated equation)
5. Conclusion:
- The correct equation needed to solve the word problem is:
[tex]\[
x + 12 = 20
\][/tex]
6. Result identification:
- According to the option list, this equation corresponds to option C.
Hence, the correct option is C.
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