MIT

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question:f James gets a cable program and the first 100 channels cost 100, while the next 100 channels cost half of that amount, how much did James pay in total, considering that he splits the cost evenly with his roommate?

answer:The cost of the first 100 channels is 100, so each channel costs 100/100 = 1. The cost of the next 100 channels is half of that amount, so each channel costs 1/2 = 0.50. The total cost for the first 200 channels is 100 channels x 1 + 100 channels x 0.50 = 100 + 50 = 150. James splits the cost evenly with his roommate, so he pays 150/2 = 75. James paid a total of 75. 75 The answer is: 75

question:Every bag of Dummies (a chocolate candy) contains the same number of pieces. The Dummies in one bag can't be divided equally among 9 kids, because after each kid gets the same (whole) number of pieces, 7 pieces are left over. If the Dummies in three bags are divided equally among 9 kids, what is the smallest number of pieces that could possibly be left over?

answer:If 7 pieces are left over when the Dummies in one bag are divided equally among 9 kids, then the number of Dummies in one bag is 9n+7, where n is a positive integer. If the Dummies in three bags are divided equally among 9 kids, then the number of Dummies in three bags is 3(9n+7)=27n+21. When 27n+21 is divided by 9, the remainder is 3. Therefore, the smallest number of pieces that could possibly be left over is boxed{3}.The answer is: 3

question:f Adam needs a new laptop and has two options, with the first laptop priced at 500 and the second laptop being 3 times more expensive than the first, what would be the total amount Adam would need to spend if he decides to purchase both?

answer:The first laptop is priced at 500. The second laptop is 3 times more expensive than the first, so it would be 3 * 500 = 1500. If Adam decides to purchase both laptops, the total amount he would need to spend is 500 + 1500 = 2000. 2000 The answer is: 2000

question:This weekend's football game matched the Seattle Seahawks with the Denver Broncos. The final score was 37-23, with the Seattle Seahawks taking the win. If a touchdown is worth 7 points and a field goal is worth 3 points, how many touchdowns did the Seattle Seahawks score if they scored 3 field goals during the game?

answer:The Seattle Seahawks scored 37 points in total. They scored 3 field goals, which is 3 x 3 = 9 points. To find the number of touchdowns, we need to subtract the points from field goals from the total score: 37 - 9 = 28 A touchdown is worth 7 points, so we divide the remaining points by 7: 28 / 7 = 4 Therefore, the Seattle Seahawks scored 4 touchdowns during the game. 4 The answer is: 4