To find the correct graph that represents the balance of Jackie’s cash box after selling smoothies, we need to calculate how the balance changes as she sells smoothies.
- Jackie starts with $15.
- Each smoothie costs $3.75.
- For each smoothie sold, her cash box increases by $3.75.
Let’s define the relationship mathematically:
- If x is the number of smoothies sold, then the cash box balance, y, after selling x smoothies can be calculated as: \[ y = 15 + 3.75 \cdot x \]
Now, we can calculate the balance for a few values of x:
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For x = 0: \[ y = 15 + 3.75 \cdot 0 = 15 \]
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For x = 2: \[ y = 15 + 3.75 \cdot 2 = 15 + 7.5 = 22.5 \]
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For x = 4: \[ y = 15 + 3.75 \cdot 4 = 15 + 15 = 30 \]
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For x = 6: \[ y = 15 + 3.75 \cdot 6 = 15 + 22.5 = 37.5 \]
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For x = 8: \[ y = 15 + 3.75 \cdot 8 = 15 + 30 = 45 \]
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For x = 10: \[ y = 15 + 3.75 \cdot 10 = 15 + 37.5 = 52.5 \]
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For x = 12: \[ y = 15 + 3.75 \cdot 12 = 15 + 45 = 60 \]
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For x = 14: \[ y = 15 + 3.75 \cdot 14 = 15 + 52.5 = 67.5 \]
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For x = 16: \[ y = 15 + 3.75 \cdot 16 = 15 + 60 = 75 \]
Now we can summarize the points calculated:
- (0, 15)
- (2, 22.5)
- (4, 30)
- (6, 37.5)
- (8, 45)
- (10, 52.5)
- (12, 60)
- (14, 67.5)
- (16, 75)
Since the cash box balance starts at $15 and increases consistently based on the number of smoothies sold, we compare our results with the provided options:
- Option C lists the points: (0, 15), (2, 22.5), (4, 30), (6, 37.5), (8, 45), (10, 52.5), (12, 60), (14, 67.5), and (16, 75).
Therefore, the correct answer is C.