Let's break this down step-by-step to find the appropriate equation for the number of points Tisha's academic team needs to earn in the district match, denoted as [tex]\(d\)[/tex].
1. Identify the total points needed to advance:
- The team needs a total of [tex]\(T\)[/tex] points to advance to the state finals.
2. Points from local matches:
- They have had three local matches with points [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
3. Relationship of district match points:
- Points in the district match count for twice as much as points in the local matches. Thus, the points earned in the district match is [tex]\(2d\)[/tex].
4. Setting up the equation:
- The total points [tex]\(T\)[/tex] required to advance is the sum of points from the three local matches and twice the district match points.
- Thus, we can formulate the equation: [tex]\( T = a + b + c + 2d \)[/tex].
5. Solving for [tex]\(d\)[/tex]:
- To find [tex]\(d\)[/tex], isolate it on one side of the equation. Start with the original equation:
[tex]\[
T = a + b + c + 2d
\][/tex]
- Subtract the sum of the points from the local matches:
[tex]\[
T - (a + b + c) = 2d
\][/tex]
- Finally, divide both sides by 2 to solve for [tex]\(d\)[/tex]:
[tex]\[
d = \frac{T - a - b - c}{2}
\][/tex]
So, the correct equation that will help Tisha find how many points they need to earn in the district match to advance is:
[tex]\[
d = \frac{T - a - b - c}{2}
\][/tex]
