Math Problem Statement

During the school holidays, Chris read 312 pages of a book at first. He read the remaining pages in 20 days, with the some number of pages each day. During these 20 days, he read 1/12 of the book in 6 days. How many pages did he read in the 6 days?

Solution

Let the total number of pages in the book be denoted by TT. Chris initially read 312 pages, so the remaining pages are T312T - 312. These remaining pages were read over 20 days, with the same number of pages each day.

Let pp represent the number of pages Chris read per day during the 20 days. Then, the total number of pages read in 20 days is:

p×20=T312p \times 20 = T - 312

We are also told that Chris read 112\frac{1}{12} of the book in the first 6 days of the 20-day period. The number of pages read in these 6 days is 6p6p, and this is equal to 112\frac{1}{12} of the total pages TT:

6p=112×T6p = \frac{1}{12} \times T

To solve this, first express pp in terms of TT using the second equation:

p=T12×6=T72p = \frac{T}{12 \times 6} = \frac{T}{72}

Now, substitute this value of pp into the first equation:

T72×20=T312\frac{T}{72} \times 20 = T - 312

Simplifying:

20T72=T312\frac{20T}{72} = T - 312

5T18=T312\frac{5T}{18} = T - 312

To eliminate the fraction, multiply through by 18:

5T=18(T312)5T = 18(T - 312)

Distribute the 18 on the right-hand side:

5T=18T56165T = 18T - 5616

Now, move all terms involving TT to one side:

5T18T=56165T - 18T = -5616

13T=5616-13T = -5616

Solve for TT:

T=561613=432T = \frac{5616}{13} = 432

Thus, the total number of pages in the book is 432432. Now, to find how many pages Chris read in the 6 days, use the formula for pp:

p=43272=6p = \frac{432}{72} = 6

Therefore, in 6 days, Chris read:

6p=6×6=36 pages.6p = 6 \times 6 = 36 \text{ pages}.

Final Answer:

Chris read 36 pages in 6 days.

Would you like further clarification or details on any part of the solution?


Here are 5 questions to deepen your understanding:

  1. How would the result change if Chris had read the same number of pages in 10 days instead of 6?
  2. What is the total number of pages Chris read in 20 days?
  3. How can we calculate the number of pages left after Chris read for the first 6 days?
  4. How can you generalize this method for any book with a different number of pages?
  5. How would the calculations change if Chris read 110\frac{1}{10} of the book in the first 6 days?

Tip: When solving word problems, always identify and define all the variables before setting up equations. This helps organize your approach and avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Algebra
Proportions
Linear Equations

Formulas

p * 20 = T - 312
6p = 1/12 * T
p = T / 72

Theorems

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Suitable Grade Level

Grades 6-8