A book contains 192 pages. A boy reads X complete pages every day. If he has not finished the book after 10 days, find the highest possible value of X.
Understand the Problem
The question is asking us to determine the maximum number of complete pages (X) a boy can read each day in order for him not to finish a 192-page book after 10 days. This involves setting up an inequality based on the total number of pages read in 10 days compared to 192.
Answer
19
Answer for screen readers
The maximum number of complete pages ( X ) the boy can read each day is ( 19 ).
Steps to Solve
- Set up the inequality
Let ( X ) be the maximum number of pages the boy can read each day. Since he reads for 10 days, the total pages he can read is ( 10X ). We want this to be less than the total pages in the book, which is 192. Therefore, we set up the inequality:
$$ 10X < 192 $$
- Solve for X
To find the maximum number of pages he can read each day, we need to isolate ( X ). We do this by dividing both sides of the inequality by 10:
$$ X < \frac{192}{10} $$
- Calculate the right side
Now, perform the division on the right side:
$$ X < 19.2 $$
- Determine the maximum complete pages
Since ( X ) must be a whole number, we round down to the nearest whole number because we want the maximum number of complete pages:
$$ X = 19 $$
The maximum number of complete pages ( X ) the boy can read each day is ( 19 ).
More Information
By reading 19 pages each day, the boy will read a total of ( 10 \times 19 = 190 ) pages, which is less than the total of 192 pages. This means he won't finish the book in 10 days.
Tips
- Rounding up instead of down: It's important to round down to the nearest whole number since he can only read complete pages.
- Misinterpreting the inequality as an equation: Remember that ( X ) is constrained to be less than 19.2, leading to the conclusion that ( X ) must be an integer less than this value.
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