Half of the book means 500 / 2 = 250 pages. Reading the first half took Jane 250 / 10 = 25 days. Reading the second half of the book took Jane 250 / 5 = 50 days. So in total Jane needed 25 + 50 = 75 days to read the whole book.
The answer: 75
Reverse engineering the question: Jane had a 500 page book to read. The first half of the book Jane read with a speed of 10 pages per day, and the second half with a speed of 5 pages a day. How many days did Jane spend reading this book?


Reasoning and answer: The third dig site was dated from the year 8400 / 2 = 4200 BC. Thus, the first dig site was dated from the year 4200 - 3700 = 500 BC. The second dig site was 352 years older, so it was dated from the year 500 + 352 = 852 BC.
The answer: 852
What was the question?
Question: An archaeologist discovered three dig sites from different periods in one area. The archaeologist dated the first dig site as 352 years more recent than the second dig site. The third dig site was dated 3700 years older than the first dig site. The fourth dig site was twice as old as the third dig site. The archaeologist studied the fourth dig site’s relics and gave the site a date of 8400 BC. What year did the archaeologist date the second dig site?


20 * 13 = 260 square yards. 3 * 5 = 15 square yards. 260 - 15 = 245 square yards. Archie needs 245 square yards of sod.
The answer: 245
Reverse engineering the question: Archie needs to lay sod in his backyard that measures 20 yards by 13 yards. He has a shed on it that measures 3 yards by 5 yards. How many square yards of sod will Archie need for his backyard?


Reasoning and answer: Hansel makes $30,000 and received a 10% raise so his raise is 30,000 * .10 = $3,000.00. Hansel now makes 30,000 + 3,000 = $33,000 a year. Gretel makes $30,000 and received a 15% raise so her raise is 30,000 * .15 = $4,500.00. Gretel now makes 30,000 + 4,500 = $34,500 a year. If Gretel makes $34,500 a year and Hansel makes $33,000 then Gretel makes 34,500 - 33,000 = $1,500 more a year than Hansel.
The answer: 1500
What was the question?
Question: Hansel makes $30,000 a year and just received a 10% raise. Gretel makes the same amount as Hansel but received a 15% raise. How much more money will Gretel make compared to Hansel?


Let x be the number of feet in John’s pool. 2 * x + 5 = 15. 2x = 10. x = 5.
The answer: 5
Reverse engineering the question: John's pool is 5 feet deeper than 2 times Sarah’s pool. If John’s pool is 15 feet deep, how deep is Sarah’s pool?


After Jeff swam on Saturday, there remained 98 - 27 = 71 laps. After Sunday morning’s 15 laps there remained 71 - 15 = 56 laps. Therefore, when Jeff took the break, he had 56 laps remaining.
The answer: 56
Reverse engineering the question:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
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Jeff’s swimming coach required him to swim 98 laps over the weekend. On Saturday, Jeff swam 27 laps. On Sunday morning, he swam 15 laps, took a break, then resumed practice in the afternoon. How many laps did Jeff have remaining when he took the break?