Answer :
To solve this problem, we need to find out how many tablespoons of cocoa are needed to make 72 ounces of hot chocolate, given that 3 tablespoons are needed for 12 ounces.
Let's break this down step-by-step:
1. Understand the proportion: We know that for 12 ounces of hot chocolate, 3 tablespoons of cocoa are required. This gives us the proportion:
[tex]\[
\frac{3 \text{ tablespoons}}{12 \text{ ounces}}
\][/tex]
which simplifies to:
[tex]\[
\frac{1 \text{ tablespoon}}{4 \text{ ounces}}
\][/tex]
(since [tex]\(3 \div 12 = \frac{1}{4}\)[/tex]).
2. Set up a proportional relationship: We want to find how many tablespoons (let's call this [tex]\( x \)[/tex]) are needed for 72 ounces. We can use the proportion:
[tex]\[
\frac{1 \text{ tablespoon}}{4 \text{ ounces}} = \frac{x \text{ tablespoons}}{72 \text{ ounces}}
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
1 \times 72 = 4 \times x
\][/tex]
Simplify to:
[tex]\[
72 = 4x
\][/tex]
Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{4} = 18
\][/tex]
4. Conclusion: Therefore, you need 18 tablespoons of cocoa to make 72 ounces of hot chocolate.
The correct answer is 18 tablespoons.
Let's break this down step-by-step:
1. Understand the proportion: We know that for 12 ounces of hot chocolate, 3 tablespoons of cocoa are required. This gives us the proportion:
[tex]\[
\frac{3 \text{ tablespoons}}{12 \text{ ounces}}
\][/tex]
which simplifies to:
[tex]\[
\frac{1 \text{ tablespoon}}{4 \text{ ounces}}
\][/tex]
(since [tex]\(3 \div 12 = \frac{1}{4}\)[/tex]).
2. Set up a proportional relationship: We want to find how many tablespoons (let's call this [tex]\( x \)[/tex]) are needed for 72 ounces. We can use the proportion:
[tex]\[
\frac{1 \text{ tablespoon}}{4 \text{ ounces}} = \frac{x \text{ tablespoons}}{72 \text{ ounces}}
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
1 \times 72 = 4 \times x
\][/tex]
Simplify to:
[tex]\[
72 = 4x
\][/tex]
Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{4} = 18
\][/tex]
4. Conclusion: Therefore, you need 18 tablespoons of cocoa to make 72 ounces of hot chocolate.
The correct answer is 18 tablespoons.
