To determine which coordinate pair should be plotted next for Option B to maintain the same ratio observed in the existing points, we should first analyze the ratio of oranges to dollars in the existing points of Option B:
- Point (9, 6) gives us a ratio of \( \frac{6}{9} = \frac{2}{3} \).
- Point (18, 12) gives us a ratio of \( \frac{12}{18} = \frac{2}{3} \).
- Point (27, 18) gives us a ratio of \( \frac{18}{27} = \frac{2}{3} \).
The constant ratio for Option B is \( \frac{2}{3} \), meaning for every 3 units of oranges, there are 2 units of dollars.
To find the next point, we can use the formula derived from this ratio:
\[ \text{Dollars} = \frac{2}{3} \times \text{Oranges} \]
Now, let's analyze the potential options:
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For \( (33, 24) \): \[ \frac{24}{33} \approx 0.727 \quad (\text{not } \frac{2}{3} \approx 0.667) \]
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For \( (29, 20) \): \[ \frac{20}{29} \approx 0.690 \quad (\text{not } \frac{2}{3} \approx 0.667) \]
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For \( (30, 21) \): \[ \frac{21}{30} = \frac{7}{10} \approx 0.700 \quad (\text{not } \frac{2}{3} \approx 0.667) \]
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For \( (36, 24) \): \[ \frac{24}{36} = \frac{2}{3} \quad (\text{this one fits!}) \]
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is: \[ \text{(36, 24)} \]
3 answers