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A recipe book shows measurement conversions for tablespoons to cups. It shows that $8$ tablespoons converts to $0.5$ cup and $24$ tablespoons converts to $1.5$ cups. Write an equation that shows the proportional relationship between cups and tablespoons where $c$ represents cups and $n$ represents tablespoons.

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Write and solve equations for proportional relationships

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Q. A recipe book shows measurement conversions for tablespoons to cups. It shows that

8

tablespoons converts to

0.5

cup and

24

tablespoons converts to

1.5

cups. Write an equation that shows the proportional relationship between cups and tablespoons where

c

represents cups and

n

represents tablespoons.

Identify Given Values: Step $1$ : Identify the given values from the recipe book. We know $8$ tablespoons equals $0.5$ cups and $24$ tablespoons equals $1.5$ cups.
Calculate Constant of Proportionality: Step $2$ : Calculate the constant of proportionality, $k$ , using the first set of values. $k = \frac{\text{cups}}{\text{tablespoons}} = \frac{0.5}{8}.$
Perform Division for $k$ : Step $3$ : Perform the division to find $k$ . $k = \frac{0.5}{8} = 0.0625$ .
Write Equation with $k$ : Step $4$ : Write the equation using the constant of proportionality. Since $k = 0.0625$ , the relationship between cups ( $c$ ) and tablespoons ( $n$ ) can be expressed as $c = 0.0625n$ .

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