To determine the number of visits \( v \) that Tristan can make to earn at least 110 points for a free movie ticket, we start by creating an inequality based on the points he earns.
Tristan starts with 25 points when he signs up and earns 8.5 points for each visit he makes to the movie theater. We can express the total points he has after \( v \) visits as:
\[ \text{Total points} = 25 + 8.5v \]
He needs at least 110 points, so we can set up the following inequality:
\[ 25 + 8.5v \geq 110 \]
Now we will solve this inequality for \( v \).
- Subtract 25 from both sides:
\[ 8.5v \geq 110 - 25 \]
\[ 8.5v \geq 85 \]
- Now, divide both sides by 8.5:
\[ v \geq \frac{85}{8.5} \]
- Calculate \( \frac{85}{8.5} \):
\[ v \geq 10 \]
Thus, Tristan needs to make at least 10 visits to earn his first free movie ticket. The solution to the inequality is:
\[ v \geq 10 \]
1 answer