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Answer :
To solve the problem, we need to determine how many hours Angus plans to study this week. Here are the steps:
1. Understand the Problem:
- Last week, Angus studied for [tex]\(6 \frac{1}{3}\)[/tex] hours.
- This week, he plans to study twice as much as he studied last week.
2. Convert Mixed Number to Improper Fraction:
- First, convert [tex]\(6 \frac{1}{3}\)[/tex] to an improper fraction or a decimal.
- [tex]\(6 \frac{1}{3}\)[/tex] is equal to [tex]\(6 + \frac{1}{3}\)[/tex], which is approximately [tex]\(6.333...\)[/tex].
3. Calculate Planned Study Hours:
- He plans to study 2 times as much. So, multiply the hours from last week by 2:
- [tex]\(2 \times 6.333...\)[/tex] which equals approximately [tex]\(12.666...\)[/tex].
4. Interpret the Result:
- The answer [tex]\(12.666...\)[/tex] can be converted back into a mixed number.
- [tex]\(12.666...\)[/tex] is equivalent to [tex]\(12 \frac{2}{3}\)[/tex].
Finally, Angus plans to study approximately [tex]\(12 \frac{2}{3}\)[/tex] hours this week, which does not match any of the given options (A, B, C, D). The provided options might not reflect a correct conversion, or possibly there was an oversight in listing options. But based on the calculated result, [tex]\(12 \frac{2}{3}\)[/tex] hours is the correct planned study time. If you are required to choose from the given options in a particular case, it might be best to double-check whether there is an error in the question or answer choices provided.
1. Understand the Problem:
- Last week, Angus studied for [tex]\(6 \frac{1}{3}\)[/tex] hours.
- This week, he plans to study twice as much as he studied last week.
2. Convert Mixed Number to Improper Fraction:
- First, convert [tex]\(6 \frac{1}{3}\)[/tex] to an improper fraction or a decimal.
- [tex]\(6 \frac{1}{3}\)[/tex] is equal to [tex]\(6 + \frac{1}{3}\)[/tex], which is approximately [tex]\(6.333...\)[/tex].
3. Calculate Planned Study Hours:
- He plans to study 2 times as much. So, multiply the hours from last week by 2:
- [tex]\(2 \times 6.333...\)[/tex] which equals approximately [tex]\(12.666...\)[/tex].
4. Interpret the Result:
- The answer [tex]\(12.666...\)[/tex] can be converted back into a mixed number.
- [tex]\(12.666...\)[/tex] is equivalent to [tex]\(12 \frac{2}{3}\)[/tex].
Finally, Angus plans to study approximately [tex]\(12 \frac{2}{3}\)[/tex] hours this week, which does not match any of the given options (A, B, C, D). The provided options might not reflect a correct conversion, or possibly there was an oversight in listing options. But based on the calculated result, [tex]\(12 \frac{2}{3}\)[/tex] hours is the correct planned study time. If you are required to choose from the given options in a particular case, it might be best to double-check whether there is an error in the question or answer choices provided.
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