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------------------------------------------------ A recipe book shows measurement conversions for tablespoons to cups. It shows that 8 tablespoons convert to 0.5 cup, and 24 tablespoons convert to 1.5 cups.

Write an equation that shows the proportional relationship between cups and tablespoons, where [tex]$c$[/tex] represents cups and [tex]$n$[/tex] represents tablespoons.

A. [tex]$n = 0.0625c$[/tex]

B. [tex]$c = 0.0625n$[/tex]

C. [tex]$n = \frac{0.5}{8}c$[/tex]

D. [tex]$c = \frac{8}{0.5}n$[/tex]

To create an equation showing the proportional relationship between cups ([tex]$ c $[/tex]) and tablespoons ([tex]$ n $[/tex]), we can utilize the given data points from the recipe book:

1. 8 tablespoons is equivalent to 0.5 cup.
2. 24 tablespoons is equivalent to 1.5 cups.

From these points, we can determine the conversion factor by seeing the relationship between the number of tablespoons and cups in both instances. Let's find the number of cups per tablespoon in each example:

- For the first conversion:
[tex]\[
\frac{0.5 \text{ cups}}{8 \text{ tablespoons}} = 0.0625 \text{ cups per tablespoon}
\][/tex]

- For the second conversion:
[tex]\[
\frac{1.5 \text{ cups}}{24 \text{ tablespoons}} = 0.0625 \text{ cups per tablespoon}
\][/tex]

Both calculations yield the same result, confirming the conversion factor is consistent. Therefore, the relationship is proportional.

Based on this finding, we can write the equation for the relationship between cups ([tex]$ c $[/tex]) and tablespoons ([tex]$ n $[/tex]) as:

[tex]\[
c = 0.0625n
\][/tex]

This equation means that to find the number of cups ([tex]$ c $[/tex]), you multiply the number of tablespoons ([tex]$ n $[/tex]) by 0.0625. Therefore, the correct answer is:

[tex]\[ c = 0.0625n \][/tex]