Klein read 30 pages of a book on Monday and 1/8 of the book on Tuesday. He completed the remaining 1/4 of the book on Wendesday. How many pages are there in the book?
The correct answer and explanation is:
Let’s define the total number of pages in the book as P.
Step 1: Analyze the problem statement
- On Monday, Klein read 30 pages.
- On Tuesday, he read 1/8 of the book, so he read 18P\frac{1}{8}P pages.
- On Wednesday, he read the remaining 1/4 of the book, so he read 14P\frac{1}{4}P pages.
Step 2: Express the total pages read
Klein read the entire book over three days, so the sum of pages read on Monday, Tuesday, and Wednesday equals the total number of pages PP: 30+18P+14P=P30 + \frac{1}{8}P + \frac{1}{4}P = P
Step 3: Solve the equation
First, express all terms involving PP with a common denominator: 30+18P+28P=P30 + \frac{1}{8}P + \frac{2}{8}P = P
(Since 14=28\frac{1}{4} = \frac{2}{8})
Add the fractions: 30+38P=P30 + \frac{3}{8}P = P
Subtract 38P\frac{3}{8}P from both sides to isolate the constant term: 30=P−38P30 = P – \frac{3}{8}P 30=88P−38P=58P30 = \frac{8}{8}P – \frac{3}{8}P = \frac{5}{8}P
Step 4: Solve for PP
Multiply both sides by 85\frac{8}{5}: P=30×85=30×1.6=48P = 30 \times \frac{8}{5} = 30 \times 1.6 = 48
Answer:
The total number of pages in the book is 48 pages.
Explanation (300 words):
This problem involves fractions of a whole and some fixed quantities, so the best way to solve it is by expressing all the parts Klein read as fractions of the total book length, which we call PP.
We know that Klein read a fixed number of pages on Monday (30 pages). On Tuesday and Wednesday, however, he read fractions of the book. Tuesday’s reading was 18\frac{1}{8} of the total book, and Wednesday’s was 14\frac{1}{4} of the total book. The problem states these three parts combined make up the entire book.
So, by setting up the equation: Monday’s pages+Tuesday’s pages+Wednesday’s pages=Total pages\text{Monday’s pages} + \text{Tuesday’s pages} + \text{Wednesday’s pages} = \text{Total pages}
or 30+18P+14P=P30 + \frac{1}{8}P + \frac{1}{4}P = P
we are expressing the total pages read over the three days.
Next, convert 14\frac{1}{4} to 28\frac{2}{8} to combine the Tuesday and Wednesday parts: 30+18P+28P=30+38P=P30 + \frac{1}{8}P + \frac{2}{8}P = 30 + \frac{3}{8}P = P
Rearranging terms: 30=P−38P=58P30 = P – \frac{3}{8}P = \frac{5}{8}P
Solving for PP gives us the total pages in the book: P=30×85=48P = \frac{30 \times 8}{5} = 48
Therefore, Klein’s book has 48 pages in total. This approach highlights the usefulness of expressing problems with fractions and unknowns into algebraic equations to find the unknown quantity.