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 126 pages of the novel.

(a) How many pages does the novel have?
(b) How many pages did you ready by the end of the second day?

Answer 1

A. 336

B. 210

Explanation:

To solve, we need to first multiply 126 by 2, which gives us 252. This is how many pages we had left after the first day. Then, since we read one-quarter on the first day, 252 is three-quarters, or 75% of the book. To find what number 252 is 75% of, we multiply both sides by 100 and divide by 75. This gives us 336, and the total amount. Next, we need to find how many pages we read on the first day. To do this, we find 25% of 336, which is 84. Then add 84 (how much we read on the first day) to 126 (how much we read on the second day), which gives us 210.

Answer 2

(a) 336 pages

(b) 210 pages

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Work Shown:

Part (a)

x = number of pages

x/4 = amount read on day 1

3x/4 = amount left to read after day 1 is over

(1/2)*(3x/4) = 3x/8 = amount read on day 2

(x/4) + (3x/8) = (2x/8)+(3x/8) = 5x/8 = amount read on days 1 and 2

x - (5x/8) = 8x/8 - (5x/8) = 3x/8 = amount left after day 2 is over

3x/8 = 126

3x = 8*126

3x = 1008

x = 1008/3

x = 336

There are 336 pages total

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Check:

336 pages total.

You read one-quarter of that on day one, so you read 336/4 = 84 pages on the first day.

There are 336-84 = 252 pages left (note that 3/4 * 336 = 252)

Then on day two, you read half of what's left, so you read 252/2 = 126 pages. The other half (126) is the last 126 pages mentioned for day 3, so the answer to part (a) is confirmed.

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There are at least three ways we can solve part (b)

1. Add up the number of pages read on days 1 and 2 to get 84+126 = 210 (refer to the "check" section above).
2. In the first section we found that 5x/8 represents how many pages have been read by the end of day 2. Plug in x = 336 to find that 5*336/8 = 210
3. Since we know there are 336 pages total, and 126 is what needs to be read on the third day to finish up the book, this must mean 336-126 = 210 pages have been read so far for days 1 and 2 combined.

Either way, 210 pages have been read by the end of the 2nd day.