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?

Question

What amount of kernels does serina use per cup of popcorn?

Answer 1

To determine how many tablespoons of kernels Sernina uses per cup of popcorn, we start by converting the amount of popcorn she made and the corresponding amount of kernels into a single unit.

First, let's convert the 2 1/4 cups of popcorn into an improper fraction: $$2\frac{1}{4}=\frac{9}{4}\text{ cups}$$

Next, we know she used 1 1/2 tablespoons of kernels, which can be converted to an improper fraction as well: $$1\frac{1}{2}=\frac{3}{2}\text{ tablespoons}$$

Now, we can find the amount of kernels used per cup of popcorn by dividing the total tablespoons of kernels by the total cups of popcorn: $$\text{Kernels per cup}=\frac{\text{Kernels}}{\text{Cups}}=\frac{\frac{3}{2}\text{ tablespoons}}{\frac{9}{4}\text{ cups}}$$

To divide by a fraction, we multiply by its reciprocal: $$\text{Kernels per cup}=\frac{3}{2}\times \frac{4}{9}$$

Now we perform the multiplication: $$=\frac{3\times 4}{2\times 9}=\frac{12}{18}=\frac{2}{3}\text{ tablespoons per cup}$$

Now that we know she uses $\frac{2}{3}$ tablespoons of kernels per cup of popcorn, we need to calculate how many tablespoons she needs to make 6 cups of popcorn.

We multiply the kernels per cup by the number of cups desired: $$\text{Kernels for 6 cups}=\frac{2}{3}\text{ tablespoons per cup}\times 6\text{ cups}$$ $$=\frac{2\times 6}{3}=\frac{12}{3}=4\text{ tablespoons}$$

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