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Answer :
To solve the problem, we want to determine how many tablespoons of kernels Serena needs per cup of popcorn and then find out how many tablespoons she needs to make 6 cups of popcorn.
### Step 1: Determine Kernels Per Cup
1. Initial Popcorn and Kernels Amounts:
- Serena makes [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn with [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels.
- Convert these mixed numbers to improper fractions:
- [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex] cups of popcorn
- [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex] tablespoons of kernels
2. Calculate Tablespoons of Kernels Per Cup of Popcorn:
- Divide 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 of kernels per cup of popcorn.
### Step 2: Calculate Kernels for 6 Cups
1. Determine Kernels Needed for 6 Cups of Popcorn:
- If Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon per cup, then for 6 cups:
[tex]\[
\text{Kernels for 6 cups} = 6 \times \frac{2}{3} = \frac{12}{3} = 4
\][/tex]
- Therefore, Serena needs 4 tablespoons of kernels for 6 cups of popcorn.
### Conclusion
- Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon of kernels per cup of popcorn.
- To make 6 cups of popcorn, she will need about 4 tablespoons of kernels.
This is a reasonable estimate for the amount of kernels Serena needs.
### Step 1: Determine Kernels Per Cup
1. Initial Popcorn and Kernels Amounts:
- Serena makes [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn with [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels.
- Convert these mixed numbers to improper fractions:
- [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex] cups of popcorn
- [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex] tablespoons of kernels
2. Calculate Tablespoons of Kernels Per Cup of Popcorn:
- Divide 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 of kernels per cup of popcorn.
### Step 2: Calculate Kernels for 6 Cups
1. Determine Kernels Needed for 6 Cups of Popcorn:
- If Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon per cup, then for 6 cups:
[tex]\[
\text{Kernels for 6 cups} = 6 \times \frac{2}{3} = \frac{12}{3} = 4
\][/tex]
- Therefore, Serena needs 4 tablespoons of kernels for 6 cups of popcorn.
### Conclusion
- Serena uses [tex]\(\frac{2}{3}\)[/tex] tablespoon of kernels per cup of popcorn.
- To make 6 cups of popcorn, she will need about 4 tablespoons of kernels.
This is a reasonable estimate for the amount of kernels Serena needs.
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