Tisha and her academic team are working to go to state finals. They must have a certain number of points, T, to advance. They have had three local matches, b, c and d, and will attend a district match. District match points count for four times the number of points than local matches do. Choose the equation that would help Tisha find how many points they need to earn in the district match, a, to advance.

Question

a. a equals T over 4 minus b minus c minus d
b. a equals T minus b minus c minus d all over 4
c. a equals T plus b plus c plus d all over 4
d. a = 4(T − b − c − d)

Answer 1

To find the number of points Tisha and her team need to earn in the district match, we start with the requirement that they need a total of \( T \) points to advance.

They have already earned points in three local matches: \( b \), \( c \), and \( d \).

In the district match, the points earned \( a \) count as four times the points of a local match. So, the contribution of the points \( a \) from the district match should be effectively treated as \( 4a \) when considering the total points.

We set up the equation for total points like this:

\[ 4a + b + c + d = T \]

Now, we want to solve for \( a \):

1. Subtract \( b \), \( c \), and \( d \) from both sides:

\[ 4a = T - b - c - d \]

2. Divide both sides by 4:

\[ a = \frac{T - b - c - d}{4} \]

This matches option b from your choices:

b. \( a = \frac{T - b - c - d}{4} \)

So the correct equation that would help Tisha find how many points they need to earn in the district match is:

b. a equals T minus b minus c minus d all over 4.