To determine which equation or tape diagram correctly represents the context described, let's break down the information:
- Initial Points: Violet receives 45 points just for signing up.
- Points Earned Per Visit: She earns 2.5 points for each visit to the movie theater.
- Points Needed for a Free Ticket: She needs 75 points to earn a free movie ticket.
- Let \( v \) represent the number of visits she makes.
Now, we can formulate the equation based on this information:
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The total points Violet has after making \( v \) visits can be expressed as: \[ \text{Total Points} = \text{Initial Points} + (\text{Points per Visit} \times \text{Number of Visits}) \] This translates to: \[ \text{Total Points} = 45 + 2.5v \]
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She needs a total of 75 points for a free movie ticket, hence: \[ 45 + 2.5v = 75 \]
Therefore, the correct equation is: \[ 2.5v + 45 = 75 \]
Now let's look at the multiple choice options:
A: \( 2.5 + 45v = 75 \) — This is incorrect because it misplaces the variable \( v \).
B: \( 2.5(v + 45) = 75 \) — This is incorrect because it suggests multiplying the points per visit by the total points instead of adding them.
C: This seems to represent a tape diagram in a non-standard format, but there aren't specific amounts indicated that could portray the equation accurately.
D: This describes a tape diagram showing multiple instances of 2.5 (representing points earned per visit) and starting with 45. The setup might not be perfectly clear from this alone.
Based on the explanations, the most appropriate representation that correctly captures the situation (out of those given) is A: \[ 2.5v + 45 = 75. \]
However, seeing none of these options perfectly presents that equation directly, the closest equivalent that frames equation correctly in context is none of the options. But in a structured selection, if you consider the balance of points, D might depict a clearer idea of points accumulation comparatively, despite its ambiguity.
Final choice tends to lean towards:
- D (assuming it has elements of correct accumulation to point needs)
If you strictly want an accurate equation form: None of the provided ones fit precisely, the original form \(45 + 2.5v = 75\) is not present specifically in your options.
So, I would suggest selecting option AA, if option D provides clear iterations holding value of v alongside rest but none are perfectly matching. Check correspondence against context if clarified or adjusted further.
1 answer