Question

On the first day of vacation, you read one-quarter of a novel. On the second day, you read half of the remaining pages. On the third day, you read the last 123 pages of the novel.

(a) How many pages does the novel have?
pages

(b) How many pages did you read by the end of the second day?
pages

Answer 1

The novel has 328 pages. By the end of the second day, the student had read 205 pages of the novel.

Step-by-step explanation:

The student's schoolwork question can be addressed by setting up and solving algebraic equations. Let's denote the total number of pages in the novel as x. On the first day, one-quarter of the novel is read, which is x/4 pages. So, there are 3x/4 pages remaining. On the second day, half of the remaining pages are read, which is (1/2) × (3x/4) = 3x/8 pages. On the third day, the student reads the last 123 pages, which were all the pages that were left. Therefore, the equation to solve for x is:

x - (x/4 + 3x/8) = 123

We can solve this equation to find out the total number of pages in the novel:

First, let's find a common denominator for the fractions. It is 8.

8x/8 - (2x/8 + 3x/8) = 123

8x/8 - 5x/8 = 123

3x/8 = 123

Let's multiply both sides of the equation by 8/3 to solve for x.

x = 123 × (8/3)

x = 328

The novel has 328 pages.

To find out how many pages were read by the end of the second day, we add the amount read on the first and second days:

(x/4) + (3x/8) = (2x/8) + (3x/8) = 5x/8

5x/8 when x = 328 is:

(5 × 328)/8 = 205

By the end of the second day, 205 pages were read.

Answer 2

328 pages for the novel

123 pages for the second day

Step-by-step explanation:

Let the number of pages of the novel = x

Raw Equation

(1/4)x + 1/2 (3/4)x + 123 = x

Solution

(1/4)x + (3/8)x+ 123 = x

Change the fractions to common denominators.

(2/8)x + (3/8)x + 123 = x

Add the fractions.

(2/8 + 3/8)x + 123 = x

Subtract (5/8)x from both sides.

(5/8)x + 123 = x

(5/8)x- (5/8)x + 123 = x - (5/8)x

Multiply both sides by 8

123 = (3/8)x

123 * 8 = 3x

Divide by 3

984 = 3x

984/3 = 3x / 3

328 = x

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At the end of the second day, she read 3/8 * 328 = 123 pages.