To set up an equation to represent the context, we want to consider Violet's initial points and the points she earns per visit.
Violet starts with 45 points and earns 2.5 points for each visit to the movie theater. She needs a total of 75 points to earn a free movie ticket.
Let's represent the number of visits Violet makes as \( v \). The total points Violet has after making \( v \) visits can be expressed as:
\[ \text{Total points} = 45 + 2.5v \]
We want to know when her total points will be at least 75, so we can set up the equation:
\[ 45 + 2.5v = 75 \]
This equation can be solved for \( v \) to find out how many visits she must make to earn enough points for a free movie ticket.
Alternatively, you could represent this situation using a tape diagram:
- Draw a tape that represents 75 points.
- Mark 45 points on this tape to represent the points Violet currently has.
- The remainder of the tape (from 45 to 75) will represent the points she still needs, which is \( 75 - 45 = 30 \) points.
- Since she earns 2.5 points for each visit, you can divide the remaining 30 points by 2.5 to find out how many visits she needs to make.
In summary:
- The equation is \( 45 + 2.5v = 75 \).
- A tape diagram can represent this by showing her current points, the needed points, and the points earned per visit.
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