Math Problem Statement

A pile of 40 books of the same kind was 92.8 cm high. A few books were removed from the top of the pile and the height of the remaining books was 81.2 cm. How many books were removed?

Solution

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Question 8:

A pile of 40 books is 92.8 cm high. Some books were removed, reducing the pile height to 81.2 cm. How many books were removed?

  1. Calculate the height of one book: Height of one book=Total heightTotal books=92.840=2.32cm\text{Height of one book} = \frac{\text{Total height}}{\text{Total books}} = \frac{92.8}{40} = 2.32 \, \text{cm}

  2. Calculate the number of books corresponding to the remaining height: Remaining books=New heightHeight of one book=81.22.3235books\text{Remaining books} = \frac{\text{New height}}{\text{Height of one book}} = \frac{81.2}{2.32} \approx 35 \, \text{books}

  3. Subtract the remaining books from the total books: Books removed=4035=5\text{Books removed} = 40 - 35 = 5

Answer: 5 books were removed.


Question 9:

Cindy left home at 8:45 a.m. Her walk to the station took 0.3 hours, and her train ride took 24 minutes. She waited 112\frac{1}{12} of an hour at the station. What time did she arrive at her destination?

  1. Convert 0.3 hours to minutes: 0.3hours=0.3×60=18minutes0.3 \, \text{hours} = 0.3 \times 60 = 18 \, \text{minutes}

  2. Add the walking and train travel times in minutes: 18minutes+24minutes=42minutes18 \, \text{minutes} + 24 \, \text{minutes} = 42 \, \text{minutes}

  3. Convert 112\frac{1}{12} of an hour to minutes: 112hours=112×60=5minutes\frac{1}{12} \, \text{hours} = \frac{1}{12} \times 60 = 5 \, \text{minutes}

  4. Add the waiting time to the total: 42minutes+5minutes=47minutes42 \, \text{minutes} + 5 \, \text{minutes} = 47 \, \text{minutes}

  5. Add 47 minutes to 8:45 a.m.: 8:45+47minutes=9:32a.m.8:45 + 47 \, \text{minutes} = 9:32 \, \text{a.m.}

Answer: Cindy arrived at her destination at 9:32 a.m.


Question 10:

The vet and two cats weigh 92.456 kg together. If each cat weighs 2.350 kg, how much does the vet weigh?

  1. Calculate the total weight of the two cats: Weight of two cats=2.350×2=4.700kg\text{Weight of two cats} = 2.350 \times 2 = 4.700 \, \text{kg}

  2. Subtract the cats' weight from the total weight: Vet’s weight=92.4564.700=87.756kg\text{Vet's weight} = 92.456 - 4.700 = 87.756 \, \text{kg}

Answer: The vet weighs 87.756 kg.


Do you want further clarifications or detailed explanations for any of these solutions?

Here are 5 related questions to practice:

  1. If another 3 books were removed in Question 8, what would the new pile height be?
  2. How many minutes in total did Cindy spend waiting, walking, and traveling in Question 9?
  3. If Cindy's train journey time was doubled, what would her new arrival time be?
  4. What is the percentage of the vet's weight relative to the total weight in Question 10?
  5. If each book in Question 8 weighed 1.5 kg, what is the total weight of the pile initially?

Tip: Break down problems into small steps for better accuracy and understanding.

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Math Problem Analysis

Mathematical Concepts

Proportional Reasoning
Division
Subtraction

Formulas

Height of one book = Total height / Total books
Remaining books = New height / Height of one book
Books removed = Total books - Remaining books

Theorems

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Suitable Grade Level

Grades 5-7