To determine the dollar value of the raffle prize given the relationship [tex]\( T - 6P = 100 \)[/tex] and the expected number of tickets sold [tex]\( T = 1900 \)[/tex], we need to solve for [tex]\( P \)[/tex].
1. Substitute the given value of [tex]\( T \)[/tex] into the equation:
[tex]\[
1900 - 6P = 100
\][/tex]
2. Rearrange the equation to isolate the term with [tex]\( P \)[/tex]:
[tex]\[
1900 - 100 = 6P
\][/tex]
[tex]\[
1800 = 6P
\][/tex]
3. Solve for [tex]\( P \)[/tex] by dividing both sides of the equation by 6:
[tex]\[
P = \frac{1800}{6}
\][/tex]
[tex]\[
P = 300
\][/tex]
Therefore, the dollar value of the raffle prize is [tex]\(\$ 300\)[/tex].
The correct answer is:
b. [tex]\(\$ 300\)[/tex]
