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

Answer:

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.