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Answer :
To determine a reasonable estimate for the amount of kernels Serena needs to make 6 cups of popcorn, follow these steps:
1. Understand the initial ratio:
- Serena made [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn using [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels.
2. Convert mixed numbers to improper fractions or decimals:
- [tex]\(2 \frac{1}{4}\)[/tex] cups is equivalent to 2.25 cups.
- [tex]\(1 \frac{1}{2}\)[/tex] tablespoons is equivalent to 1.5 tablespoons.
3. Calculate the unit rate:
- Determine how many tablespoons of kernels are needed per cup of popcorn.
- Divide the tablespoons of kernels by the cups of popcorn:
[tex]\[
\frac{1.5 \text{ tablespoons}}{2.25 \text{ cups}} \approx 0.6667 \text{ tablespoons per cup}
\][/tex]
4. Calculate the amount of kernels needed for 6 cups of popcorn:
- Multiply the unit rate by 6 cups:
[tex]\[
0.6667 \times 6 \approx 4.0 \text{ tablespoons}
\][/tex]
5. Conclusion:
- A reasonable estimate for the amount of kernels Serena needs to make 6 cups of popcorn is about 4 tablespoons of kernels.
1. Understand the initial ratio:
- Serena made [tex]\(2 \frac{1}{4}\)[/tex] cups of popcorn using [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of kernels.
2. Convert mixed numbers to improper fractions or decimals:
- [tex]\(2 \frac{1}{4}\)[/tex] cups is equivalent to 2.25 cups.
- [tex]\(1 \frac{1}{2}\)[/tex] tablespoons is equivalent to 1.5 tablespoons.
3. Calculate the unit rate:
- Determine how many tablespoons of kernels are needed per cup of popcorn.
- Divide the tablespoons of kernels by the cups of popcorn:
[tex]\[
\frac{1.5 \text{ tablespoons}}{2.25 \text{ cups}} \approx 0.6667 \text{ tablespoons per cup}
\][/tex]
4. Calculate the amount of kernels needed for 6 cups of popcorn:
- Multiply the unit rate by 6 cups:
[tex]\[
0.6667 \times 6 \approx 4.0 \text{ tablespoons}
\][/tex]
5. Conclusion:
- A reasonable estimate for the amount of kernels Serena needs to make 6 cups of popcorn is about 4 tablespoons of kernels.
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