Question
A chef makes 30 muffins using 12 cups of flour. the number of muffins is directly proportional to the number of cups of flour. what is the constant of proportionality?
Answers
GPT-4o mini
To find the constant of proportionality in this scenario, we can use the relationship between the number of muffins and the cups of flour.
The chef makes 30 muffins using 12 cups of flour, which we can express as the ratio of muffins to cups of flour:
\[
\text{Number of muffins} = k \times \text{Cups of flour}
\]
where \( k \) is the constant of proportionality. Using the values provided:
\[
30 = k \times 12
\]
To find \( k \), we can rearrange this equation:
\[
k = \frac{30}{12}
\]
Now, we simplify this fraction:
\[
k = \frac{5}{2} = 2.5
\]
Thus, the constant of proportionality is \( 2.5 \). This means that for every cup of flour used, 2.5 muffins are produced.
The chef makes 30 muffins using 12 cups of flour, which we can express as the ratio of muffins to cups of flour:
\[
\text{Number of muffins} = k \times \text{Cups of flour}
\]
where \( k \) is the constant of proportionality. Using the values provided:
\[
30 = k \times 12
\]
To find \( k \), we can rearrange this equation:
\[
k = \frac{30}{12}
\]
Now, we simplify this fraction:
\[
k = \frac{5}{2} = 2.5
\]
Thus, the constant of proportionality is \( 2.5 \). This means that for every cup of flour used, 2.5 muffins are produced.