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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]

Answer :

To solve this problem, we need to establish a proportional relationship between cups [tex]\( c \)[/tex] and tablespoons [tex]\( n \)[/tex].

Let's analyze the given measurement conversions:

1. 8 tablespoons correspond to 0.5 cup.
2. 24 tablespoons correspond to 1.5 cups.

The goal is to find an equation that represents this proportional relationship.

### Step 1: Understand the relationship

For a proportional relationship, the ratio between the two quantities remains constant. This constant is known as the proportional constant. We can determine the proportional constant using the given conversions.

### Step 2: Calculate the proportional constant from each conversion

- For the first conversion (8 tablespoons = 0.5 cup):

- The ratio of cups to tablespoons is [tex]\( \frac{0.5}{8} \)[/tex].
- Simplifying this, we get [tex]\( 0.0625 \)[/tex].

- For the second conversion (24 tablespoons = 1.5 cups):

- The ratio of cups to tablespoons is [tex]\( \frac{1.5}{24} \)[/tex].
- Simplifying this, we also get [tex]\( 0.0625 \)[/tex].

### Step 3: Establish the equation

Since the proportional constant is consistent (i.e., it is the same for both conversions), we can write the equation for the relationship. The relationship is described by:

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

### Final Answer

The equation that shows the proportional relationship between cups and tablespoons is:

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

This means for every tablespoon, you multiply by 0.0625 to get the equivalent in cups.

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Rewritten by : Barada