Question
Which real-world scenario is true? (1 point) You need to complete 15 math lessons. If you complete 3 1/2 math lessons today and 4 1/2 lessons per day after that, you can complete your lessons in 7 more days. You need to complete 15 math lessons. If you complete 3 1/2 math lessons today and 4 1/2 lessons per day after that, you can complete the lessons in 3 more days. You need to complete 15 math lessons. If you complete 4 1/2 math lessons today and 3 1/2 lessons per day after that, you can complete the lessons in 4 more days. You need to complete 15 math lessons. If you complete 4 1/2 math lessons today and 3 1/2 lessons per day after that. you can complete the lessons in 3 more days. and do the answer in fraction form
Answers
GPT-4o mini
Let’s analyze each scenario step-by-step using fractions.
1. **Scenario 1:**
- Today: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons
- Daily: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons for 7 days.
Total lessons completed:
\[
\frac{7}{2} + 7 \cdot \frac{9}{2} = \frac{7}{2} + \frac{63}{2} = \frac{70}{2} = 35
\]
This exceeds 15 lessons, so this scenario does not hold.
2. **Scenario 2:**
- Today: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons
- Daily: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons for 3 days.
Total lessons completed:
\[
\frac{7}{2} + 3 \cdot \frac{9}{2} = \frac{7}{2} + \frac{27}{2} = \frac{34}{2} = 17
\]
This exceeds 15 lessons, so this scenario does not hold.
3. **Scenario 3:**
- Today: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons
- Daily: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons for 4 days.
Total lessons completed:
\[
\frac{9}{2} + 4 \cdot \frac{7}{2} = \frac{9}{2} + \frac{28}{2} = \frac{37}{2} = 18.5
\]
This exceeds 15 lessons, so this scenario does not hold.
4. **Scenario 4:**
- Today: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons
- Daily: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons for 3 days.
Total lessons completed:
\[
\frac{9}{2} + 3 \cdot \frac{7}{2} = \frac{9}{2} + \frac{21}{2} = \frac{30}{2} = 15
\]
This is exactly 15 lessons, so this scenario holds true.
Therefore, the true scenario is **Scenario 4**: You need to complete 15 math lessons. If you complete \(4 \frac{1}{2}\) math lessons today and \(3 \frac{1}{2}\) lessons per day after that, you can complete the lessons in 3 more days.
1. **Scenario 1:**
- Today: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons
- Daily: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons for 7 days.
Total lessons completed:
\[
\frac{7}{2} + 7 \cdot \frac{9}{2} = \frac{7}{2} + \frac{63}{2} = \frac{70}{2} = 35
\]
This exceeds 15 lessons, so this scenario does not hold.
2. **Scenario 2:**
- Today: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons
- Daily: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons for 3 days.
Total lessons completed:
\[
\frac{7}{2} + 3 \cdot \frac{9}{2} = \frac{7}{2} + \frac{27}{2} = \frac{34}{2} = 17
\]
This exceeds 15 lessons, so this scenario does not hold.
3. **Scenario 3:**
- Today: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons
- Daily: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons for 4 days.
Total lessons completed:
\[
\frac{9}{2} + 4 \cdot \frac{7}{2} = \frac{9}{2} + \frac{28}{2} = \frac{37}{2} = 18.5
\]
This exceeds 15 lessons, so this scenario does not hold.
4. **Scenario 4:**
- Today: Complete \(4 \frac{1}{2} = \frac{9}{2}\) lessons
- Daily: Complete \(3 \frac{1}{2} = \frac{7}{2}\) lessons for 3 days.
Total lessons completed:
\[
\frac{9}{2} + 3 \cdot \frac{7}{2} = \frac{9}{2} + \frac{21}{2} = \frac{30}{2} = 15
\]
This is exactly 15 lessons, so this scenario holds true.
Therefore, the true scenario is **Scenario 4**: You need to complete 15 math lessons. If you complete \(4 \frac{1}{2}\) math lessons today and \(3 \frac{1}{2}\) lessons per day after that, you can complete the lessons in 3 more days.