Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]