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question:Last month, a factory made 12000 dolls and their associated accessories. The accessories for each doll included 2 shoes, 3 bags, 1 set of cosmetics, and 5 hats. If each doll took 45 seconds to make and each accessory took x seconds to make, what was the total combined machine operation time, in seconds, required to manufacture all of the dolls and their accessories? If we know the answer to the above question is 1860000, what is the value of unknown variable x?
answer:We know that each doll took 45 seconds to make. For each doll, there were 2 shoes, 3 bags, 1 set of cosmetics, and 5 hats as accessories. If each accessory took x seconds to make, then the total time to make the accessories for each doll is 2x + 3x + x + 5x = 11x. The total time to make the dolls and their accessories is the product of the number of dolls and the time to make each doll, plus the product of the number of dolls and the time to make the accessories for each doll: 12000 * 45 + 12000 * 11x. We are given that the total combined machine operation time is 1860000 seconds, so we can write: 12000 * 45 + 12000 * 11x = 1860000. Simplifying the left side, we get: 540000 + 132000x = 1860000. Subtracting 540000 from both sides, we get: 132000x = 1320000. Dividing both sides by 132000, we get: x = 10. The value of x is 10. 10 The answer is: 10
question:f John works 12 hours every other day and receives a 30% raise from his previous 20 an hour job, what is his monthly income in a 30-day month?
answer:John works 12 hours every other day, so he works 12 * 15 = 180 hours in a 30-day month. He received a 30% raise from his previous 20 an hour job, so his new hourly rate is 20 + (20 * 0.30) = 26 an hour. Therefore, his monthly income is 180 hours * 26 = 4680. 4680 The answer is: 4680
question:A tank can hold 100 liters of water. At the beginning of the rainy season, the tank is 2/5 filled with water. On the first day of the rainy season, the tank collected 15 liters of water. On the second day, 5 liters more water was collected than on the first day. On the third day, the tank was already filled. How many liters of water were collected on the third day?
answer:The tank is initially 2/5 filled with water, which is 2/5 x 100 liters = 40 liters. On the first day of the rainy season, 15 liters of water was collected, so the tank now has 40 + 15 = 55 liters of water. On the second day, 5 liters more water was collected than on the first day, so the tank collected 15 + 5 = 20 liters of water. The total amount of water in the tank after the second day is now 55 + 20 = 75 liters. Since the tank was already filled on the third day, the amount of water collected on the third day is 100 - 75 = 25 liters. 25 The answer is: 25
question:Alexander was 50 inches on his 8th birthday. If he grows x a foot a year, how many inches tall will he be on his 12th birthday? If we know the answer to the above question is 74, what is the value of unknown variable x?
answer:Alexander was 50 inches tall on his 8th birthday. If he grows x a foot a year, then in 4 years he will grow 4x feet. Since there are 12 inches in a foot, his growth in inches will be 4x * 12 = 48x inches. To find out how tall he will be on his 12th birthday, we add his initial height and his growth: 50 + 48x. We are given that he will be 74 inches tall on his 12th birthday, so we can write: 50 + 48x = 74. Solving for x, we get: x = 1/2. The value of x is 1/2. 1 The answer is: 1