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

Answer 1

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.