Question

Sernina makes 2 1/4 cups of popcorn using 1 1/2 tablespoons of kernels. She wants to know how many tablespoons of kernals to use to make 6 cups of popcorn?
What amount of kernels does serina use per cup of popcorn?

What amount of kernels does she need to make 6 cups of popcorn?

Answer 1

To determine how many tablespoons of kernels Sernina uses per cup of popcorn, we first need to convert the total number of cups of popcorn she makes into a form where we can calculate the amount of kernels used per cup.

1. **Convert the cups of popcorn to an improper fraction:**
- \(2 \frac{1}{4}\) cups = \(2 \times 4 + 1 = 8 + 1 = 9/4\) cups.

2. **Calculate the amount of kernels used per cup:**
- Sernina uses \(1 \frac{1}{2}\) tablespoons of kernels, which can also be converted to an improper fraction:
- \(1 \frac{1}{2} = 1 \times 2 + 1 = 2 + 1 = 3/2\) tablespoons of kernels.
- Now, we can find the amount of kernels used per cup:
\[
\text{Kernels per cup} = \frac{\text{Total kernels}}{\text{Total cups}} = \frac{3/2 \text{ tablespoons}}{9/4 \text{ cups}}.
\]
- To divide by a fraction, multiply by the reciprocal:
\[
\text{Kernels per cup} = \frac{3/2}{9/4} = \frac{3}{2} \times \frac{4}{9} = \frac{12}{18} = \frac{2}{3} \text{ tablespoons per cup}.
\]

3. **Calculate the total amount of kernels needed for 6 cups of popcorn:**
- Now that we know Sernina uses \( \frac{2}{3} \) tablespoons of kernels per cup, we can find the amount for 6 cups:
\[
\text{Total kernels for 6 cups} = 6 \times \frac{2}{3} = \frac{12}{3} = 4 \text{ tablespoons}.
\]

### Summary:
- **Amount of kernels used per cup of popcorn:** \( \frac{2}{3} \) tablespoons.
- **Total amount of kernels needed for 6 cups of popcorn:** 4 tablespoons.