The rope was cut into 2 + 3 = 5 parts. So each part is 40 / 5 = 8 meters long. Since the shorter part is consists of 2 parts, then it is 8 x 2 = 16 meters long.
The answer: 16
Reverse engineering the question: A 40 meters rope was cut into 2 parts in the ratio of 2:3. How long is the shorter part?


Reasoning and answer: There are 12 months in 1 year and his loan is for 5 years so that's 12 * 5 = 60 months. His monthly payment is $150.00 and he pays this for 60 months so his loan for the tractor was 150 * 60 = $9,000.00.
The answer: 9000
What was the question?
Question: Gunther just financed a John Deere tractor through the dealership. If his monthly payment is $150.00 a month, for 5 years, with no interest, how much did he finance the tractor for?


The cost of 9 plates is $2 x 9 = $18. So, Chenny paid $24 - $18 = $6 for the spoons. Therefore, she bought $6 / $1.50 = 4 spoons.
The answer: 4
Reverse engineering the question: Chenny bought 9 plates at $2 each. She also bought spoons at $1.50 each. How many spoons did Chenny buy if she paid a total of $24 for the plates and spoon?


Reasoning and answer: Labor cost is .5 * 60 = 30 dollars per hour. The cost for parts is 20 * 2 = $40. The total cost for labor is 220 - 40 = $180. He spent 180 / 30 = 6 hours on labor.
The answer: 6
What was the question?
Question: Mark spent 220 dollars to fix his car. It needed two parts that cost 20 dollars each, and labor cost .5 dollars a minute. How many hours did the mechanic work?


There were a total of 30 x 100 = 3000 tickets ordered by the school organizers. The 4th graders bought 3000 x 30 / 100 = 900 tickets. So, there were 3000 - 900 = 2100 tickets left for the other two grade levels. The 5th graders bought 2100 x 50 / 100 = 1050 tickets. So, 2100 - 1050 = 1050 tickets were left then. Since 100 tickets were bought by the 6th graders, therefore 1050 - 100 = 950 tickets were left unsold.
The answer: 950
Reverse engineering the question: For the funfair, the school organizers ordered 30 rolls of tickets. Each roll of tickets has 100 tickets. The 4th graders bought 30% of the tickets while the 5th graders bought 50% of the remaining tickets. Then the 6th graders bought a total of 100 tickets. How many tickets were left unsold?


There were 2 * 500 = 1000 people at the counting station who were counted on the first day. In the two days, 1000 + 500 = 1500 were counted at the station.
The answer: 1500
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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At a people counting station, the number of people counted on the first day was twice the total number counted on the second day. If 500 people were counted on the second day, how many people were counted on the two days?