Answer :
To find out how many tablespoons of kernels Serena needs to make 6 cups of popcorn, let's follow these steps:
1. Determine the Ratio of Kernels to Popcorn:
Serena makes [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn with [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels. First, let's convert those mixed numbers into improper fractions:
- [tex]\(2 \frac{1}{4}\)[/tex] cups is equivalent to [tex]\(\frac{9}{4}\)[/tex] cups.
- [tex]\(1 \frac{1}{2}\)[/tex] tablespoons is equivalent to [tex]\(\frac{3}{2}\)[/tex] tablespoons.
2. Calculate the Unit Rate:
Now we find out how many tablespoons of kernels are used per cup of popcorn by dividing the amount of kernels by the amount of popcorn:
[tex]\[
\text{Kernels per cup} = \frac{\frac{3}{2}}{\frac{9}{4}} = \frac{3}{2} \times \frac{4}{9} = \frac{12}{18} = \frac{2}{3}
\][/tex]
So, Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon(s) of kernels per cup of popcorn.
3. Find the Amount of Kernels Needed for 6 Cups:
To find out how many tablespoons are needed for 6 cups of popcorn, multiply the unit rate by 6:
[tex]\[
\text{Kernels needed} = \frac{2}{3} \times 6 = 4
\][/tex]
Therefore, Serena needs 4 tablespoons of kernels to make 6 cups of popcorn.
By following these steps, it's determined that Serena needs 4 tablespoons of kernels to make 6 cups of popcorn.
1. Determine the Ratio of Kernels to Popcorn:
Serena makes [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn with [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels. First, let's convert those mixed numbers into improper fractions:
- [tex]\(2 \frac{1}{4}\)[/tex] cups is equivalent to [tex]\(\frac{9}{4}\)[/tex] cups.
- [tex]\(1 \frac{1}{2}\)[/tex] tablespoons is equivalent to [tex]\(\frac{3}{2}\)[/tex] tablespoons.
2. Calculate the Unit Rate:
Now we find out how many tablespoons of kernels are used per cup of popcorn by dividing the amount of kernels by the amount of popcorn:
[tex]\[
\text{Kernels per cup} = \frac{\frac{3}{2}}{\frac{9}{4}} = \frac{3}{2} \times \frac{4}{9} = \frac{12}{18} = \frac{2}{3}
\][/tex]
So, Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon(s) of kernels per cup of popcorn.
3. Find the Amount of Kernels Needed for 6 Cups:
To find out how many tablespoons are needed for 6 cups of popcorn, multiply the unit rate by 6:
[tex]\[
\text{Kernels needed} = \frac{2}{3} \times 6 = 4
\][/tex]
Therefore, Serena needs 4 tablespoons of kernels to make 6 cups of popcorn.
By following these steps, it's determined that Serena needs 4 tablespoons of kernels to make 6 cups of popcorn.
