Answer :
Sure, let's break down this problem step-by-step to find how many tablespoons of kernels Serena needs to make 6 cups of popcorn.
1. Understand the initial ratio:
Serena makes [tex]\(2 \frac{1}{4}\)[/tex] (which is 2.25) cups of popcorn using [tex]\(1 \frac{1}{2}\)[/tex] (which is 1.5) tablespoons of kernels. So the ratio of tablespoons of kernels to cups of popcorn is:
[tex]\[
\text{Ratio} = \frac{1.5 \text{ tablespoons}}{2.25 \text{ cups}}
\][/tex]
2. Calculate the number of tablespoons per cup:
Simplify the ratio to find the number of tablespoons per one cup of popcorn:
[tex]\[
\frac{1.5}{2.25} = \frac{1.5 \div 1.5}{2.25 \div 1.5} = \frac{1}{1.5}
\][/tex]
3. Convert ratio to a better form:
Simplify [tex]\(\frac{1}{1.5}\)[/tex]:
[tex]\[
\frac{1}{1.5} = \frac{1 \div 1.5}{1.5 \div 1.5} = \frac{1}{1.5} = \frac{2}{3} \text{ tablespoons per cup}
\][/tex]
4. Find total tablespoons for 6 cups of popcorn:
Multiply the number of tablespoons per cup by the total number of cups:
[tex]\[
\text{Tablespoons for 6 cups} = \frac{2}{3} \times 6
\][/tex]
5. Perform the multiplication:
[tex]\[
\frac{2}{3} \times 6 = 4 \text{ tablespoons}
\][/tex]
So, Serena needs about 4 tablespoons of kernels to make 6 cups of popcorn. Hence, the correct estimate is:
[tex]\[
\boxed{4 \text{ tablespoons of kernels}}
\][/tex]
1. Understand the initial ratio:
Serena makes [tex]\(2 \frac{1}{4}\)[/tex] (which is 2.25) cups of popcorn using [tex]\(1 \frac{1}{2}\)[/tex] (which is 1.5) tablespoons of kernels. So the ratio of tablespoons of kernels to cups of popcorn is:
[tex]\[
\text{Ratio} = \frac{1.5 \text{ tablespoons}}{2.25 \text{ cups}}
\][/tex]
2. Calculate the number of tablespoons per cup:
Simplify the ratio to find the number of tablespoons per one cup of popcorn:
[tex]\[
\frac{1.5}{2.25} = \frac{1.5 \div 1.5}{2.25 \div 1.5} = \frac{1}{1.5}
\][/tex]
3. Convert ratio to a better form:
Simplify [tex]\(\frac{1}{1.5}\)[/tex]:
[tex]\[
\frac{1}{1.5} = \frac{1 \div 1.5}{1.5 \div 1.5} = \frac{1}{1.5} = \frac{2}{3} \text{ tablespoons per cup}
\][/tex]
4. Find total tablespoons for 6 cups of popcorn:
Multiply the number of tablespoons per cup by the total number of cups:
[tex]\[
\text{Tablespoons for 6 cups} = \frac{2}{3} \times 6
\][/tex]
5. Perform the multiplication:
[tex]\[
\frac{2}{3} \times 6 = 4 \text{ tablespoons}
\][/tex]
So, Serena needs about 4 tablespoons of kernels to make 6 cups of popcorn. Hence, the correct estimate is:
[tex]\[
\boxed{4 \text{ tablespoons of kernels}}
\][/tex]
