Let's analyze the problem step by step.
1. Define the Variables:
- Let [tex]\( c \)[/tex] represent Central's score before they scored a three-pointer.
- Eastern's score before the three-pointer is then [tex]\( 2c \)[/tex] since they had double the score of Central.
2. Calculate Central's Final Score:
- Central scored a three-pointer just as the game ended. Therefore, their final score is [tex]\( c + 3 \)[/tex].
3. Calculate the Total Score in the Game:
- The total score in the game is the sum of Central's score after the three-pointer and Eastern's score.
- Central's final score is [tex]\( c + 3 \)[/tex].
- Eastern's score is [tex]\( 2c \)[/tex].
- Therefore, the total score in the game can be expressed as:
[tex]\[
(c + 3) + 2c = 3c + 3
\][/tex]
4. Verify which Expressions Match the Total Score:
Now, we will compare the total score expression [tex]\( 3c + 3 \)[/tex] with the given expressions to find the matching ones.
- The first given expression is [tex]\( 2c + c \)[/tex]:
[tex]\[
2c + c = 3c
\][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The second given expression is [tex]\( 3c + 3 \)[/tex]:
[tex]\[
3c + 3
\][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
- The third given expression is [tex]\( 2c + 3 \)[/tex]:
[tex]\[
2c + 3
\][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fourth given expression is [tex]\( 2c + c - 3 \)[/tex]:
[tex]\[
2c + c - 3 = 3c - 3
\][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fifth given expression is [tex]\( 2c - c + 3 \)[/tex]:
[tex]\[
2c - c + 3 = c + 3
\][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The sixth given expression is [tex]\( 2c + c + 3 \)[/tex]:
[tex]\[
2c + c + 3 = 3c + 3
\][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
Therefore, the matching expressions for the total score are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
To summarize:
- The total points scored in the game is expressed as [tex]\( 3c + 3 \)[/tex].
- The matching expressions are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
