Answer :
Sure! Let's solve the problem step-by-step.
### (a) How many tablespoons of butter will you need for 0.3 teaspoons of baking powder?
1. Understand the Original Proportion:
- You have a recipe that includes 0.5 teaspoons of baking powder and 1 cup of butter.
- We know that 1 cup of butter is equivalent to 8 tablespoons.
2. Determine the Proportional Relationship:
- For the given 0.5 teaspoons of baking powder, 8 tablespoons of butter are used.
3. Set up the Proportion:
- To find how many tablespoons of butter are needed for 0.3 teaspoons of baking powder, we use the proportion:
[tex]\[
\frac{8 \text{ tablespoons}}{0.5 \text{ teaspoons}} = \frac{x \text{ tablespoons}}{0.3 \text{ teaspoons}}
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[
8 \times 0.3 = 0.5 \times x
\][/tex]
- Simplify:
[tex]\[
2.4 = 0.5x
\][/tex]
- Divide both sides by 0.5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{2.4}{0.5} = 4.8
\][/tex]
- Therefore, you will need 4.8 tablespoons of butter.
### (b) How many tablespoons of baking powder will you need for 5 cups of flour?
1. Understand the Original Proportion:
- The original recipe uses 0.5 teaspoons of baking powder for 3 cups of flour.
2. Determine How Much Baking Powder is Needed Per Cup:
- Calculate the amount of baking powder per cup of flour:
[tex]\[
\frac{0.5 \text{ teaspoons}}{3 \text{ cups}} \approx 0.1667 \text{ teaspoons per cup}
\][/tex]
3. Calculate for 5 Cups of Flour:
- Multiply the amount per cup by 5 cups:
[tex]\[
0.1667 \times 5 \approx 0.8335 \text{ teaspoons}
\][/tex]
4. Convert Teaspoons to Tablespoons:
- Remember, 1 tablespoon = 3 teaspoons.
- Convert the teaspoons to tablespoons:
[tex]\[
\frac{0.8335}{3} \approx 0.2778
\][/tex]
- Therefore, you'll need about 0.2778 tablespoons of baking powder.
That's how you solve both parts of the problem!
### (a) How many tablespoons of butter will you need for 0.3 teaspoons of baking powder?
1. Understand the Original Proportion:
- You have a recipe that includes 0.5 teaspoons of baking powder and 1 cup of butter.
- We know that 1 cup of butter is equivalent to 8 tablespoons.
2. Determine the Proportional Relationship:
- For the given 0.5 teaspoons of baking powder, 8 tablespoons of butter are used.
3. Set up the Proportion:
- To find how many tablespoons of butter are needed for 0.3 teaspoons of baking powder, we use the proportion:
[tex]\[
\frac{8 \text{ tablespoons}}{0.5 \text{ teaspoons}} = \frac{x \text{ tablespoons}}{0.3 \text{ teaspoons}}
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[
8 \times 0.3 = 0.5 \times x
\][/tex]
- Simplify:
[tex]\[
2.4 = 0.5x
\][/tex]
- Divide both sides by 0.5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{2.4}{0.5} = 4.8
\][/tex]
- Therefore, you will need 4.8 tablespoons of butter.
### (b) How many tablespoons of baking powder will you need for 5 cups of flour?
1. Understand the Original Proportion:
- The original recipe uses 0.5 teaspoons of baking powder for 3 cups of flour.
2. Determine How Much Baking Powder is Needed Per Cup:
- Calculate the amount of baking powder per cup of flour:
[tex]\[
\frac{0.5 \text{ teaspoons}}{3 \text{ cups}} \approx 0.1667 \text{ teaspoons per cup}
\][/tex]
3. Calculate for 5 Cups of Flour:
- Multiply the amount per cup by 5 cups:
[tex]\[
0.1667 \times 5 \approx 0.8335 \text{ teaspoons}
\][/tex]
4. Convert Teaspoons to Tablespoons:
- Remember, 1 tablespoon = 3 teaspoons.
- Convert the teaspoons to tablespoons:
[tex]\[
\frac{0.8335}{3} \approx 0.2778
\][/tex]
- Therefore, you'll need about 0.2778 tablespoons of baking powder.
That's how you solve both parts of the problem!
