On day one Conner collects 32 rocks because 8 x 4 = 32. On day three Sydney collects 64 because 32 x 2 = 64. After three days Sydney has 915 rocks because 837 + 0 + 4 + 64 = 905. Before the third day Conner has 878 because 723 + 32 + 123 = 878. Conner needs to collect 37 on day three to tie Sydney because 905 - 878 = 27.
The answer: 27
Reverse engineering the question: Sydney and Conner are having a three day rock collecting contest to see who can have the largest collection after adding to their existing collections. Before they start, Sydney has 837 rocks and Conner has 723. On day one, Sydney collects 4 rocks and Conner collects 8 times as many. On day two Sydney rests and Conner collects 123. On the third day, Sydney collects twice as many as Conner did on the first day. How many does Conner have to collect on day three to make sure he at least ties Sydney?
Reasoning and answer: First find the total cost of the drink tickets: 5 tickets * $7 / ticket = $35. Then add that cost to the cost of the ticket to find the total cost: $35 + $181 = $216. Then multiply Jenna's hourly rate by the number of hours she works each week to find her weekly earnings: $18 / hour * 30 hours / week = $540 / week. Then multiply her weekly earnings by the number of weeks she works each month: $540 / week * 4 weeks / month = $2160 / month. Then divide the cost of the concert by Jenna's monthly earnings and multiply by 100% to express the answer as a percentage: $216 / $2160 * 100% = 10%.
The answer: 10
What was the question?
Question: Jenna wants to buy a concert ticket that costs $181, plus five drink tickets for $7 each. If Jenna earns $18 an hour and works 30 hours a week, what percentage of her monthly salary will she spend on this outing?
They need to rotate 1,600 times because 8 x 200 = 1,600. They need to rotate 1,000 more times because 1,600 - 600 = 1,000.
The answer: 1000
Reverse engineering the question: Greg is riding his bike around town and notices that each block he rides, his wheels rotate 200 times. He's now on a a trail and wants to make sure he rides at least 8 blocks. His wheels have already rotated 600 times, how many more times do they need to rotate to reach his goal?
Reasoning and answer: Thomas has been saving for six years, and since each year has 12 months, he has been making savings for 6 * 12 = 72 months. Since Thomas has been saving $40 in the bank every month for six years, he has saved 72 * $40 = $2880. Joseph has been saving 2 / 5 times less money per month than Thomas, meaning he has been saving 2 / 5 * $40 = $16 less per month. The total amount of money that Joseph has been saving per month is $40 - $16 = $24. In six years, Joseph has saved $24 * 72 = $1728. Together, they have saved a total of $2880 + $1728 = $4608.
The answer: 4608
What was the question?
Question: Thomas has been saving $40 in the bank every month for six years. His friend Joseph has been saving 2/5 times less money per month. How much money are they having in their savings account altogether?
On the first day, they traveled 5 * 7 = 35 miles. On the first part of the second day, they traveled 6 * 6 = 36 miles. The second part of the second day, at half their morning speed, they traveled (6 / 2) * 3 = 9 miles. On the final day, they traveled 5 * 7 = 35 miles. In total, they traveled 35 + 36 + 9 + 35 = 115 miles.
The answer: 115
Reverse engineering the question: Barry and his friend, Jim, went horseback riding across central Texas. They traveled at 5 miles per hour for 7 hours, and then stopped for the evening. The next day, they traveled at 6 miles per hour for 6 hours, and then at half that speed for another three hours, before stopping to rest for the night. On the third and final day, they traveled for 5 hours at 7 miles per hour. In total, how far did they travel, in miles, during their horseback riding trip?
If Tom could triple his reading speed, he could read 12 * 3 = 36 pages of a book in one hour. Therefore, during two hours he could read 36 * 2 = 72 pages.
The answer: 72
Reverse engineering the question:
During one hour, Tom can read 12 pages of a book. How many pages would he be able to read during 2 hours if he could increase his reading speed by a factor of 3?