The cost of each key chain in packs of 10 for $20 is $20 / 10 = $2. The cost of each key chain in packs of 4 for $12 is $12 / 4 = $3. There is a price difference of $3 - $2 = $1 per key chain between the two choices. By buying 20 key chains at a lower price, Matt can save 20x$1 = $20.
The answer: 20
Reverse engineering the question: Matt can buy key chains in packs of 10 for $20 or in packs of 4 for $12. How much money can he save if he chooses to buy 20 key chains at a lower price?


Reasoning and answer: The second movie was 2 * .5 = 1` hour longer than the first movie. So the second movie was 2 + 1 = 3 hours long. That means the first two movies had a combined time of 3 + 2 = 5 hours. So the last movie had a length of 5 - 1 = 4 hours. That means the marathon lasted 5 + 4 = 9 hours.
The answer: 9
What was the question?
Question: Tim decides to do a movie marathon. The first movie is 2 hours long. The next movie is 50% longer. And the last movie is 1 hour shorter than the combined time of the previous 2 movies. How long was his movie marathon?


The patch is 16 * 20 = 320 square feet. So he needs 320 / 4 = 80 patches. The first 10 patches cost 10 * 10 = $100. He gets a discount on the next 80 - 10 = 70 patches. They each cost 10 / 2 = $5. So in total they cost 70 * 5 = $350. That means in total he paid 100 + 350 = $450.
The answer: 450
Reverse engineering the question: James wants to build a 16-foot by 20-foot quilt. He uses patches that are each 4 square feet. The first 10 patches cost $10 each and then each patch after that cost half as much. How much do the patches for the quilt cost?


Reasoning and answer: First find how many eagle feathers he found: 17 * 6 feathers = 102 feathers. Then add the number of hawk feathers he found: 102 feathers + 6 feathers = 108 feathers. Then subtract the number of feathers Jerry gave to his sister: 108 feathers - 10 feathers = 98 feathers. Then divide that number by 2 to find how many feathers Jerry has left: 98 feathers / 2 = 49 feathers.
The answer: 49
What was the question?
Question: Jerry finds six hawk feathers and 17 times as many eagle feathers as hawk feathers. If he gives 10 feathers to his sister and sells half the remaining feathers, how many does he have left?


Combining January and February, Sara sent 6 + 9 = 15 letters. In March, she sent 3 * 6 = 18 letters. Altogether, Sara sent 15 + 18 = 33 letters.
The answer: 33
Reverse engineering the question: Sara sent letters to her friend in China every month. She sent 6 letters in January, 9 letters in February, and in March she sent triple the number of letters she sent in January. How many letters does Sara send?


It takes Lara 7 minutes and 23 seconds to make it through the obstacle course the first time. 7 minutes x 60 seconds per minute = 420 seconds + 23 seconds = 443 seconds to get through the first part of the obstacle course. The second stage of the obstacle course she completes in 73 seconds + 443 seconds = 516 seconds. It takes 5 minutes and 58 seconds for Lara to get through the obstacle course the second time. 5 minutes x 60 seconds per minute = 300 + 58 seconds = 358 seconds. Combined, it takes Lara 516 + 358 seconds = 874 seconds for Lara to run the whole obstacle course.
The answer: 874
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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Lara is a contestant on a fun game show where she needs to navigate an inflated bouncy house obstacle course. First she needs to carry a backpack full of treasure through the obstacle course and set it down on the other side, which she does in 7 minutes and 23 seconds. Second, she needs to crank open the door to the obstacle course so she can go back through, which takes her 73 seconds. After she gets through the door she traverses the obstacle course again and makes it out faster without the backpack, in 5 minutes and 58 seconds. How many seconds total does it take her to complete the obstacle course?