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?

Answer 1

To find out how many tablespoons of kernels Sernina needs to make 6 cups of popcorn, we first need to determine the ratio of popcorn made to the number of tablespoons of kernels used.

1. **Convert mixed numbers to improper fractions:**
- \( 2 \frac{1}{4} \) cups can be converted as follows:
\[
2 \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ cups}
\]
- \( 1 \frac{1}{2} \) tablespoons can be converted as follows:
\[
1 \frac{1}{2} = \frac{3}{2} \text{ tablespoons}
\]

2. **Determine the ratio of popcorn to kernels:**
- The ratio of cups of popcorn to tablespoons of kernels is:
\[
\text{Ratio} = \frac{\frac{9}{4} \text{ cups}}{\frac{3}{2} \text{ tablespoons}} = \frac{9}{4} \times \frac{2}{3} = \frac{9 \times 2}{4 \times 3} = \frac{18}{12} = \frac{3}{2}
\]
- This means that for every \( \frac{3}{2} \) tablespoons of kernels, Sernina makes \( \frac{9}{4} \) cups of popcorn.

3. **Calculate how many tablespoons are needed for 6 cups:**
- Now we need to find how many tablespoons correspond to 6 cups of popcorn:
\[
\frac{9}{4} \text{ cups corresponds to } \frac{3}{2} \text{ tablespoons}
\]
- To find how many tablespoons \( x \) are needed for 6 cups, we set up the ratio:
\[
\frac{9/4}{3/2} = \frac{6}{x}
\]

4. **Cross multiply to solve for \( x \):**
\[
(9/4)x = (3/2)(6)
\]
- Calculate the right side:
\[
(3/2) \times 6 = \frac{18}{2} = 9
\]
- Now set up the equation:
\[
\frac{9}{4}x = 9
\]

5. **Isolate \( x \):**
\[
x = 9 \times \frac{4}{9} = 4
\]

Thus, Sernina needs **4 tablespoons** of kernels to make 6 cups of popcorn.