Answer :
To find the proportional relationship between cups (c) and tablespoons (n), we need to establish a consistent ratio between the two measurements based on the given information.
From the recipe book, we have the following conversions:
- 8 tablespoons is equivalent to 0.5 cups.
- 24 tablespoons is equivalent to 1.5 cups.
Step-by-step, we will determine the relationship between cups and tablespoons:
1. Start with the given conversion: 8 tablespoons = 0.5 cups.
2. We want to express cups (c) in terms of tablespoons (n).
3. Notice that a proportional relationship typically takes the form of [tex]\( c = k \cdot n \)[/tex] or [tex]\( n = k \cdot c \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
4. For sizes such as these, you can derive the constant [tex]\( k \)[/tex] by rearranging the relation to solve it. In the first case, to express [tex]\( n \)[/tex] in terms of [tex]\( c \)[/tex]:
[tex]\[
c = \frac{1}{\left(\frac{0.5}{8}\right)} n
\][/tex]
5. Calculate the constant [tex]\( \frac{0.5}{8} \)[/tex]. By dividing 0.5 by 8, we get 0.0625.
6. Check to see if the other conversion provided (24 tablespoons and 1.5 cups) maintains the same proportionality:
[tex]\[
24 = 0.0625 \times 1.5 \quad \Rightarrow \quad 24 \cdot 0.0625 = 1.5
\][/tex]
It maintains the proportion, reinforcing that this is correct.
Therefore, the correct equation that shows the proportional relationship is:
[tex]\[ c = 0.0625n \][/tex]
This equation indicates that for every tablespoon (n), there are 0.0625 cups (c). Alternatively, you can express it as:
[tex]\[ n = \frac{c}{0.0625} \][/tex]
From the recipe book, we have the following conversions:
- 8 tablespoons is equivalent to 0.5 cups.
- 24 tablespoons is equivalent to 1.5 cups.
Step-by-step, we will determine the relationship between cups and tablespoons:
1. Start with the given conversion: 8 tablespoons = 0.5 cups.
2. We want to express cups (c) in terms of tablespoons (n).
3. Notice that a proportional relationship typically takes the form of [tex]\( c = k \cdot n \)[/tex] or [tex]\( n = k \cdot c \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
4. For sizes such as these, you can derive the constant [tex]\( k \)[/tex] by rearranging the relation to solve it. In the first case, to express [tex]\( n \)[/tex] in terms of [tex]\( c \)[/tex]:
[tex]\[
c = \frac{1}{\left(\frac{0.5}{8}\right)} n
\][/tex]
5. Calculate the constant [tex]\( \frac{0.5}{8} \)[/tex]. By dividing 0.5 by 8, we get 0.0625.
6. Check to see if the other conversion provided (24 tablespoons and 1.5 cups) maintains the same proportionality:
[tex]\[
24 = 0.0625 \times 1.5 \quad \Rightarrow \quad 24 \cdot 0.0625 = 1.5
\][/tex]
It maintains the proportion, reinforcing that this is correct.
Therefore, the correct equation that shows the proportional relationship is:
[tex]\[ c = 0.0625n \][/tex]
This equation indicates that for every tablespoon (n), there are 0.0625 cups (c). Alternatively, you can express it as:
[tex]\[ n = \frac{c}{0.0625} \][/tex]
