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Tisha and her academic team are working to go to state finals. They must have a certain number of points, [tex]\( T \)[/tex], to advance. They have had three local matches, [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], and will attend a district match. District match points count for twice the number of points as local matches.

Choose the equation that would help Tisha find how many points they need to earn in the district match, [tex]\( d \)[/tex], to advance.

A. [tex]\( d = \frac{T - a - b - c}{2} \)[/tex]

B. [tex]\( d = \frac{T}{2} - a - b - c \)[/tex]

C. [tex]\( d = \frac{T + a + b + c}{2} \)[/tex]

D. [tex]\( d = 2(T - a - b - c) \)[/tex]



Answer :

GinnyAnswer
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]

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