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question:There are x workers producing chairs in a furniture factory. Each of them produces 4 chairs an hour. As a group, they produce an additional chair every 6 hours. In total, how many chairs have been produced after 6 hours? If we know the answer to the above question is 73, what is the value of unknown variable x?
answer:We know that each worker produces 4 chairs an hour, so in 6 hours, each worker would produce 4 * 6 = 24 chairs. There are x workers, so in 6 hours, all the workers would produce x * 24 chairs. In addition, as a group, they produce an additional chair every 6 hours, so in 6 hours, they would produce x additional chairs. The total number of chairs produced after 6 hours is the sum of the chairs produced by the workers and the additional chairs: x * 24 + x. We are given that the total number of chairs produced after 6 hours is 73, so we can write: x * 24 + x = 73. Simplifying the left side, we get: 25x = 73. Dividing both sides by 25, we get: x = 2.92. Since the number of workers cannot be a decimal, we can round x to the nearest whole number. The value of x is 3. 3 The answer is: 3
question:Jay & Gloria were hosting a 4th of July party at their house. Jay invited 22 people and Gloria invited 36. They wanted to buy small American flags for everyone. The craft store was having a sale on small flags, 5 flags for x. If they wanted all of their guests to have a flag and they also wanted 1 flag each, how much would they spend at the craft store? If we know the answer to the above question is 12, what is the value of unknown variable x?
answer:Jay invited 22 people and Gloria invited 36, so they have a total of 22 + 36 = 58 guests. They want to buy small American flags for everyone, so they need 58 flags. The craft store is selling 5 flags for x, so they need 58/5 = 11.6 sets of 5 flags. Since they can't buy a fraction of a set, they will need to buy 12 sets of 5 flags. The total cost of the flags would be 12 * x. We are given that the total cost is 12, so we can write: 12 * x = 12. Dividing both sides by 12, we get: x = 1. The value of x is 1. 1 The answer is: 1
question:Joan is preparing sandwiches for a family potluck. She decides to make ham sandwiches and grilled cheese sandwiches. One ham sandwich requires 2 slices of cheese, and one grilled cheese sandwich requires 3 slices of cheese. She uses a total of 50 slices of cheese to make the sandwiches. If she makes 10 ham sandwiches, how many grilled cheese sandwiches does she make?
answer:One ham sandwich requires 2 slices of cheese, so 10 ham sandwiches will require 10 * 2 = 20 slices of cheese. Since she used a total of 50 slices of cheese, this means she used 50 - 20 = 30 slices of cheese for the grilled cheese sandwiches. One grilled cheese sandwich requires 3 slices of cheese, so she made 30 / 3 = 10 grilled cheese sandwiches. 10 The answer is: 10
question:Tom decides to lease a car. He drives 50 miles on Monday, Wednesday, and Friday, and Sunday for the rest of the days he drives 100 miles. He has to pay .1 per mile he drives. He also has to pay a weekly fee of 100. How much does he have to pay in a year.
answer:Tom drives 50 miles on Monday, Wednesday, and Friday, and Sunday, so he drives a total of 4 days x 50 miles = 200 miles. For the rest of the days, he drives 100 miles, so he drives a total of 7 days - 4 days = 3 days x 100 miles = 300 miles. In a week, Tom drives a total of 200 miles + 300 miles = 500 miles. Tom has to pay .1 per mile he drives, so he has to pay 500 miles x .1 = 50 for his weekly mileage. He also has to pay a weekly fee of 100, so his total weekly payment is 100 + 50 = 150. In a year, there are 52 weeks, so Tom has to pay a total of 52 weeks x 150 = 7800. 7800 The answer is: 7800