Math Problem Statement

Machine A can print 1,500 pages/hour. How many pages will Machine B print in 20 days, working 12 hours per day if it is twice as efficient as Machine A?

Solution

The problem provided is as follows:

Problem 22: Machine A can print 1,500 pages per hour. How many pages will Machine B print in 20 days, working 12 hours per day if it is twice as efficient as Machine A?

Let's break this down:

  1. Machine A prints 1,500 pages per hour.
  2. Machine B is twice as efficient as Machine A, meaning it prints 2×1,500=3,0002 \times 1,500 = 3,000 pages per hour.
  3. Machine B works 12 hours per day for 20 days.

Calculation:

The total number of pages Machine B can print is given by: Total Pages=Pages per hour×Hours per day×Number of days\text{Total Pages} = \text{Pages per hour} \times \text{Hours per day} \times \text{Number of days}

Substituting the known values: Total Pages=3,000×12×20\text{Total Pages} = 3,000 \times 12 \times 20

Let me calculate this.Machine B will print a total of 720,000 pages in 20 days, working 12 hours per day.

The correct answer is not listed in the provided options, which means there might be an error in the choices or a miscalculation in their presentation.

Do you need further details or clarifications?

Here are 5 related questions to expand on the topic:

  1. How would the total number of pages change if Machine B worked only 10 hours per day?
  2. What if Machine B was only 1.5 times as efficient as Machine A instead of twice as efficient?
  3. How many pages would Machine A print in 20 days working 12 hours per day?
  4. How many hours would Machine B need to print 1,000,000 pages?
  5. If Machine B worked for 25 days instead of 20, how many pages would it print?

Tip: Always double-check the question options to ensure consistency with your calculated results.

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Math Problem Analysis

Mathematical Concepts

Multiplication
Efficiency
Time Calculation

Formulas

Efficiency of Machine B = 2 * Efficiency of Machine A
Total Pages = Pages per hour * Hours per day * Number of days

Theorems

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Suitable Grade Level

Grades 6-8