Answer :
To determine which option would produce a solution with the same concentration as Rebecca's, let's follow these steps:
1. Understand Rebecca's Concentration:
- Rebecca uses [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of baking soda with 3 tablespoons of hydrogen peroxide.
- First, convert [tex]\(1 \frac{1}{2}\)[/tex] into an improper fraction or decimal: [tex]\(1 \frac{1}{2} = 1.5\)[/tex].
- The concentration is calculated as the amount of baking soda divided by the amount of hydrogen peroxide, which is [tex]\( \frac{1.5}{3} = 0.5 \)[/tex].
2. Calculate Concentrations for Each Option:
- Option A: [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with 6 tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{0.75}{6} = 0.125\)[/tex].
- Option B: 3 tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{3}{1.5} = 2.0\)[/tex].
- Option C: [tex]\(1 \frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(3 \frac{1}{4}\)[/tex] tbsp of hydrogen peroxide.
- Convert [tex]\(1 \frac{3}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex] to decimals: [tex]\(1.75\)[/tex] and [tex]\(3.25\)[/tex].
- Concentration = [tex]\(\frac{1.75}{3.25} \approx 0.538\)[/tex].
- Option D: [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{0.75}{1.5} = 0.5\)[/tex].
- Option E: [tex]\(2 \frac{1}{2}\)[/tex] tbsp of baking soda with 4 tbsp of hydrogen peroxide.
- Convert [tex]\(2 \frac{1}{2}\)[/tex] to a decimal: [tex]\(2.5\)[/tex].
- Concentration = [tex]\(\frac{2.5}{4} = 0.625\)[/tex].
3. Compare each concentration with Rebecca's concentration of 0.5.
From the calculated concentrations, Option D has a concentration of 0.5, which matches Rebecca's concentration. Therefore, the answer is:
Option D: dissolving [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
1. Understand Rebecca's Concentration:
- Rebecca uses [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of baking soda with 3 tablespoons of hydrogen peroxide.
- First, convert [tex]\(1 \frac{1}{2}\)[/tex] into an improper fraction or decimal: [tex]\(1 \frac{1}{2} = 1.5\)[/tex].
- The concentration is calculated as the amount of baking soda divided by the amount of hydrogen peroxide, which is [tex]\( \frac{1.5}{3} = 0.5 \)[/tex].
2. Calculate Concentrations for Each Option:
- Option A: [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with 6 tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{0.75}{6} = 0.125\)[/tex].
- Option B: 3 tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{3}{1.5} = 2.0\)[/tex].
- Option C: [tex]\(1 \frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(3 \frac{1}{4}\)[/tex] tbsp of hydrogen peroxide.
- Convert [tex]\(1 \frac{3}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex] to decimals: [tex]\(1.75\)[/tex] and [tex]\(3.25\)[/tex].
- Concentration = [tex]\(\frac{1.75}{3.25} \approx 0.538\)[/tex].
- Option D: [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
- Concentration = [tex]\(\frac{0.75}{1.5} = 0.5\)[/tex].
- Option E: [tex]\(2 \frac{1}{2}\)[/tex] tbsp of baking soda with 4 tbsp of hydrogen peroxide.
- Convert [tex]\(2 \frac{1}{2}\)[/tex] to a decimal: [tex]\(2.5\)[/tex].
- Concentration = [tex]\(\frac{2.5}{4} = 0.625\)[/tex].
3. Compare each concentration with Rebecca's concentration of 0.5.
From the calculated concentrations, Option D has a concentration of 0.5, which matches Rebecca's concentration. Therefore, the answer is:
Option D: dissolving [tex]\(\frac{3}{4}\)[/tex] tbsp of baking soda with [tex]\(1 \frac{1}{2}\)[/tex] tbsp of hydrogen peroxide.
