After reading 3/4 of a book on Monday, 1/5 of the remainder on Tuesday and 10 pages on Wednesday. Jack still has 42 pages of the book left. How many pages did he read on Monday?
Let's start by finding out how many pages Jack had left after reading 3/4 of the book on Monday.
If we let x be the total number of pages in the book, then Jack read:
3/4 x
pages on Monday.
This means he had:
x - (3/4)x = (1/4)x
pages left.
On Tuesday, he read 1/5 of this remaining amount, which is:
(1/5) * (1/4)x = (1/20)x
pages.
After Tuesday, he had:
(1/4)x - (1/20)x = (1/5)x
pages left.
Finally, on Wednesday, he read 10 pages, leaving him with:
(1/5)x - 10 = 42
pages.
Solving for x, we get:
(1/5)x = 52
x = 260
So the total number of pages in the book is 260.
To find out how many pages Jack read on Monday, we just need to substitute x = 260 into the equation we found earlier:
3/4 x = 3/4 * 260 = 195
So Jack read 195 pages on Monday.
Let's break down the steps to find the number of pages Jack read on Monday:
Step 1: Calculate the remaining pages after reading 3/4 of the book on Monday:
Let's assume the total number of pages in the book is represented by "x".
The number of pages remaining after reading 3/4 of the book on Monday is (1 - 3/4) * x = 1/4 * x.
Step 2: Calculate the remaining pages after reading 1/5 of the remainder on Tuesday:
The number of pages remaining after reading 1/5 of the remainder on Tuesday is (1 - 1/5) * (1/4) * x = 4/5 * 1/4 * x = 1/5 * x.
Step 3: Calculate the remaining pages after reading 10 pages on Wednesday:
The number of pages remaining after reading 10 pages on Wednesday is 1/5 * x - 10.
Step 4: Set up the equation using the information given:
According to the problem, the remaining pages after Wednesday is 42.
So, we have the equation: 1/5 * x - 10 = 42.
Step 5: Solve the equation:
Adding 10 to both sides of the equation gives: 1/5 * x = 52.
Multiplying both sides by 5 gives: x = 260.
Step 6: Calculate the number of pages Jack read on Monday:
Substitute the value of "x" into the equation found in Step 1:
(1/4) * x = (1/4) * 260 = 65.
Therefore, Jack read 65 pages of the book on Monday.