To determine which coordinate pair should be plotted next for Option B to keep the ratio the same, we first need to identify the pattern in the existing points for Option B: (9, 6), (18, 12), and (27, 18).
We can see that for Option B, as the number of oranges increases, the dollars also increase, and we can calculate the ratio of dollars to oranges:
- For (9, 6): Ratio = 6 / 9 = 2/3
- For (18, 12): Ratio = 12 / 18 = 2/3
- For (27, 18): Ratio = 18 / 27 = 2/3
The consistent ratio is 2/3. To find the next coordinate point, we can maintain this ratio.
Let \( x \) be the number of oranges for the next point, then the dollars \( y \) can be expressed as:
\[ y = \frac{2}{3} x \]
We can plug in the possible options to see which one maintains this ratio:
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For (33, 24): \[ 24 \div 33 = 0.727 \quad (\text{Not } \frac{2}{3}) \]
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For (36, 24): \[ 24 \div 36 = 0.667 \quad (\text{This is } \frac{2}{3}) \]
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For (30, 21): \[ 21 \div 30 = 0.7 \quad (\text{Not } \frac{2}{3}) \]
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For (29, 20): \[ 20 \div 29 \approx 0.689 \quad (\text{Not } \frac{2}{3}) \]
The only coordinate pair that maintains the ratio of \( \frac{2}{3} \) is (36, 24).
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is:
(36, 24).
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