A recipe book shows measurement conversions for tablespoons to cups. It states 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]c = 0.0625n[/tex]
B. [tex]n = \frac{0.5}{8}c[/tex]
C. [tex]c = \frac{8}{0.5}n[/tex]

We are given two conversion facts:

1. [tex]$8$[/tex] tablespoons equals [tex]$0.5$[/tex] cups.
2. [tex]$24$[/tex] tablespoons equals [tex]$1.5$[/tex] cups.

We can set up a proportional relationship between cups ([tex]$c$[/tex]) and tablespoons ([tex]$n$[/tex]) using a constant conversion factor, say [tex]$k$[/tex], such that

[tex]$$
c = k \, n.
$$[/tex]

To determine [tex]$k$[/tex], we use the first conversion:

[tex]$$
k = \frac{c}{n} = \frac{0.5}{8} = 0.0625.
$$[/tex]

To be sure, we verify with the second conversion:

[tex]$$
\frac{1.5}{24} = 0.0625.
$$[/tex]

Since both conversions give the same factor, the proportional relationship is valid and the constant of proportionality is [tex]$0.0625$[/tex].

Thus, the equation that relates cups and tablespoons is

[tex]$$
c = 0.0625 \, n.
$$[/tex]