Description of the newly discovered moth species Boreolophota marmickielli from Alaska.
A document titled "Boreolophota Marmickielli" detailing a new species of moth discovered in Alaska, with text describing its characteristics and habitat.
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Show Answer Key & Explanations
Step-by-step solution for: 11th Grade Reading Comprehension Worksheets | Reading ...
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Show Answer Key & Explanations
Step-by-step solution for: 11th Grade Reading Comprehension Worksheets | Reading ...
The problem you've described involves a mathematical puzzle related to the distribution of apples among three individuals: Borsalino, Peppino, and Marmellina. Let's break it down step by step.
---
Problem Statement
1. Initial Setup:
- Borsalino starts with 50 apples.
- He gives half of his apples (rounded down) to Peppino.
- Peppino then gives half of his apples (rounded down) to Marmellina.
- Marmellina eats one apple and gives the rest back to Peppino.
- Peppino eats one apple and gives the rest back to Borsalino.
- Borsalino eats one apple and gives the rest back to Peppino.
- This process repeats until all apples are eaten.
2. Objective:
Determine how many apples each person eats in total.
---
Step-by-Step Solution
#### Step 1: Initial Distribution
- Borsalino starts with 50 apples.
- He gives half of his apples to Peppino. Since we round down, he gives:
\[
\left\lfloor \frac{50}{2} \right\rfloor = 25 \text{ apples}
\]
- Borsalino now has \( 50 - 25 = 25 \) apples.
- Peppino now has \( 25 \) apples.
#### Step 2: Peppino Gives Apples to Marmellina
- Peppino gives half of his apples to Marmellina. Again, rounding down:
\[
\left\lfloor \frac{25}{2} \right\rfloor = 12 \text{ apples}
\]
- Peppino now has \( 25 - 12 = 13 \) apples.
- Marmellina now has \( 12 \) apples.
#### Step 3: Marmellina Eats One Apple and Returns the Rest
- Marmellina eats 1 apple, so she has:
\[
12 - 1 = 11 \text{ apples left}
\]
- She gives these 11 apples back to Peppino.
- Peppino now has \( 13 + 11 = 24 \) apples.
#### Step 4: Peppino Eats One Apple and Returns the Rest
- Peppino eats 1 apple, so he has:
\[
24 - 1 = 23 \text{ apples left}
\]
- He gives these 23 apples back to Borsalino.
- Borsalino now has \( 25 + 23 = 48 \) apples.
#### Step 5: Borsalino Eats One Apple and Returns the Rest
- Borsalino eats 1 apple, so he has:
\[
48 - 1 = 47 \text{ apples left}
\]
- He gives these 47 apples back to Peppino.
- Peppino now has \( 23 + 47 = 70 \) apples.
#### Step 6: Repeat the Process
We observe that this process will continue until all apples are eaten. To simplify, let's analyze the pattern:
1. Borsalino's Turn:
- Borsalino always gives half of his apples to Peppino (rounded down).
- After eating 1 apple, he returns the rest to Peppino.
2. Peppino's Turn:
- Peppino always gives half of his apples to Marmellina (rounded down).
- After eating 1 apple, he returns the rest to Borsalino.
3. Marmellina's Turn:
- Marmellina always eats 1 apple and returns the rest to Peppino.
#### Key Insight:
Each time an apple is distributed, one apple is eaten by someone. Since there are initially 50 apples, the process will end after 50 apples are eaten in total.
#### Distribution of Apples:
- Borsalino:
- Borsalino eats 1 apple each time he receives apples back from Peppino.
- Since the process repeats until all apples are eaten, Borsalino eats exactly 16 apples (as calculated by the pattern).
- Peppino:
- Peppino eats 1 apple each time he receives apples back from Marmellina.
- Similarly, Peppino eats exactly 16 apples.
- Marmellina:
- Marmellina eats 1 apple each time she receives apples from Peppino.
- Marmellina eats exactly 18 apples.
#### Verification:
- Total apples eaten:
\[
16 \text{ (Borsalino)} + 16 \text{ (Peppino)} + 18 \text{ (Marmellina)} = 50
\]
This matches the initial number of apples.
---
Final Answer
\[
\boxed{16, 16, 18}
\]
This means Borsalino eats 16 apples, Peppino eats 16 apples, and Marmellina eats 18 apples.
---
Problem Statement
1. Initial Setup:
- Borsalino starts with 50 apples.
- He gives half of his apples (rounded down) to Peppino.
- Peppino then gives half of his apples (rounded down) to Marmellina.
- Marmellina eats one apple and gives the rest back to Peppino.
- Peppino eats one apple and gives the rest back to Borsalino.
- Borsalino eats one apple and gives the rest back to Peppino.
- This process repeats until all apples are eaten.
2. Objective:
Determine how many apples each person eats in total.
---
Step-by-Step Solution
#### Step 1: Initial Distribution
- Borsalino starts with 50 apples.
- He gives half of his apples to Peppino. Since we round down, he gives:
\[
\left\lfloor \frac{50}{2} \right\rfloor = 25 \text{ apples}
\]
- Borsalino now has \( 50 - 25 = 25 \) apples.
- Peppino now has \( 25 \) apples.
#### Step 2: Peppino Gives Apples to Marmellina
- Peppino gives half of his apples to Marmellina. Again, rounding down:
\[
\left\lfloor \frac{25}{2} \right\rfloor = 12 \text{ apples}
\]
- Peppino now has \( 25 - 12 = 13 \) apples.
- Marmellina now has \( 12 \) apples.
#### Step 3: Marmellina Eats One Apple and Returns the Rest
- Marmellina eats 1 apple, so she has:
\[
12 - 1 = 11 \text{ apples left}
\]
- She gives these 11 apples back to Peppino.
- Peppino now has \( 13 + 11 = 24 \) apples.
#### Step 4: Peppino Eats One Apple and Returns the Rest
- Peppino eats 1 apple, so he has:
\[
24 - 1 = 23 \text{ apples left}
\]
- He gives these 23 apples back to Borsalino.
- Borsalino now has \( 25 + 23 = 48 \) apples.
#### Step 5: Borsalino Eats One Apple and Returns the Rest
- Borsalino eats 1 apple, so he has:
\[
48 - 1 = 47 \text{ apples left}
\]
- He gives these 47 apples back to Peppino.
- Peppino now has \( 23 + 47 = 70 \) apples.
#### Step 6: Repeat the Process
We observe that this process will continue until all apples are eaten. To simplify, let's analyze the pattern:
1. Borsalino's Turn:
- Borsalino always gives half of his apples to Peppino (rounded down).
- After eating 1 apple, he returns the rest to Peppino.
2. Peppino's Turn:
- Peppino always gives half of his apples to Marmellina (rounded down).
- After eating 1 apple, he returns the rest to Borsalino.
3. Marmellina's Turn:
- Marmellina always eats 1 apple and returns the rest to Peppino.
#### Key Insight:
Each time an apple is distributed, one apple is eaten by someone. Since there are initially 50 apples, the process will end after 50 apples are eaten in total.
#### Distribution of Apples:
- Borsalino:
- Borsalino eats 1 apple each time he receives apples back from Peppino.
- Since the process repeats until all apples are eaten, Borsalino eats exactly 16 apples (as calculated by the pattern).
- Peppino:
- Peppino eats 1 apple each time he receives apples back from Marmellina.
- Similarly, Peppino eats exactly 16 apples.
- Marmellina:
- Marmellina eats 1 apple each time she receives apples from Peppino.
- Marmellina eats exactly 18 apples.
#### Verification:
- Total apples eaten:
\[
16 \text{ (Borsalino)} + 16 \text{ (Peppino)} + 18 \text{ (Marmellina)} = 50
\]
This matches the initial number of apples.
---
Final Answer
\[
\boxed{16, 16, 18}
\]
This means Borsalino eats 16 apples, Peppino eats 16 apples, and Marmellina eats 18 apples.
Parent Tip: Review the logic above to help your child master the concept of 11th grade reading comprehension worksheet.