To find a proportional relationship between the amounts of grape juice \( g \) and peach juice \( p \), we can express the relationship in the form of an equation.
We can start by checking the ratios of \( g \) to \( p \) given in the table:
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For \( g = 11.5 \) and \( p = 6.9 \): \[ \frac{g}{p} = \frac{11.5}{6.9} \approx 1.67 \]
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For \( g = 17.5 \) and \( p = 10.5 \): \[ \frac{g}{p} = \frac{17.5}{10.5} \approx 1.67 \]
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For \( g = 20.5 \) and \( p = 12.3 \): \[ \frac{g}{p} = \frac{20.5}{12.3} \approx 1.67 \]
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For \( g = 26.5 \) and \( p = 15.9 \): \[ \frac{g}{p} = \frac{26.5}{15.9} \approx 1.67 \]
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For \( g = 34.5 \) and \( p = 20.7 \): \[ \frac{g}{p} = \frac{34.5}{20.7} \approx 1.67 \]
The ratios \( \frac{g}{p} \approx 1.67 \) indicate a consistent relationship. To express this as an equation, we can say:
\[ g = kp \]
where \( k \) is the constant ratio. From the calculations, we find that \( k \approx 1.67 \).
Now let’s write the equation:
\[ g \approx 1.67p \]
This reflects the proportional relationship between the amounts of grape juice and peach juice. Alternatively, you could write it in a more precise format that captures the ratio:
\[ \frac{g}{p} \approx \frac{5}{3} \]
(based on the consistency across the values). Therefore, the final equation that accurately represents Mrs. Jones's proportional relationship is:
\[ g = \frac{5}{3} p \]
This equation describes the relationship between the amounts of grape juice and peach juice used in the smoothies.