To determine the total number of pages in the book, let's follow these steps:
1. Understand the Problem:
- The boy has read [tex]\(\frac{3}{5}\)[/tex] of the book.
- He still has 80 pages left to read.
2. Representation in Fraction:
- If [tex]\(\frac{3}{5}\)[/tex] of the book is already read, then the remaining part of the book, which is unread, is [tex]\(1 - \frac{3}{5} = \frac{2}{5}\)[/tex].
3. Relate the Unread Portion to the Total:
- The unread portion, which is [tex]\(\frac{2}{5}\)[/tex] of the book, equals 80 pages.
4. Set Up the Equation:
- Let's denote the total number of pages in the book by [tex]\(P\)[/tex].
- According to the information, [tex]\(\frac{2}{5}\)[/tex] of the total pages ([tex]\(P\)[/tex]) is equal to 80 pages.
- This can be represented as:
[tex]\[
\frac{2}{5} \times P = 80
\][/tex]
5. Solve for [tex]\(P\)[/tex]:
- To isolate [tex]\(P\)[/tex], we need to multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{5}\)[/tex], which is [tex]\(\frac{5}{2}\)[/tex]:
[tex]\[
P = 80 \times \frac{5}{2}
\][/tex]
6. Calculate the Value:
- Perform the multiplication:
[tex]\[
P = 80 \times \frac{5}{2} = 80 \times 2.5 = 200
\][/tex]
7. Conclusion:
- The total number of pages in the book is [tex]\(200\)[/tex].
Therefore, the book has 200 pages in total.
