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question:You have 5 red shirts, 5 green shirts, 6 pairs of pants, X green hats and 8 red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats? If we know the answer to the above question is 480, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. To determine the number of outfits, we need to multiply the number of choices for each item together. For the shirts, we have 5 choices (red or green). For the pants, we have 6 choices. For the hats, we have X choices for green hats and 8 choices for red hats. Since we cannot have the same color of shirts and hats, we need to consider two cases: 1. If the shirt is red, we have 5 choices for the shirt and 8 choices for the hat. So, the number of outfits in this case is 5 * 6 * 8 = 240. 2. If the shirt is green, we have 5 choices for the shirt and X choices for the hat. So, the number of outfits in this case is 5 * 6 * X = 30X. To find the total number of outfits, we add the number of outfits from each case together: 240 + 30X = 480 Subtracting 240 from both sides of the equation, we get: 30X = 240 Dividing both sides of the equation by 30, we find: X = 8 The value of X is 8. The answer is: 8
question:A lumberjack is chopping down trees so he can sell firewood. Each tree he chops produces 4 logs each, and each log is then chopped into 5 pieces of firewood. If the lumberjack has chopped 500 pieces of firewood, how many trees did he chop down?
answer:If each log is chopped into 5 pieces of firewood, then each tree produces 4 x 5 = 20 pieces of firewood. If the lumberjack has chopped 500 pieces of firewood, then he chopped down 500 / 20 = 25 trees. 25 The answer is: 25
question:need to learn vocabulary words for my Spanish exam. There are X words and the exam grade is the percentage of these words that I recall correctly. Assuming I will recall correctly the words I learn and assuming my guesses will not yield any points, The least number of words you should learn to get at least 85% on the exam is 425. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the number of vocabulary words for the Spanish exam. We know that the least number of words you should learn to get at least 85% on the exam is 425. We can set up the equation as follows: Number of words learned / Total number of words = Exam grade 425 / x = 0.85 Let's simplify and solve for x: 425 = 0.85x To isolate x, we divide both sides of the equation by 0.85: 425 / 0.85 = x 500 = x The value of x is 500. The answer is: 500
question:a Math competition, Sammy scored 20 points, Gab scored twice as many as Sammy's score, while Cher scored twice as many as Gab's score. If their opponent scored 85 points, how many more points do they have than their opponent?
answer:Gab scored twice as many as Sammy's score, so Gab scored 20 x 2 = 40 points. Cher scored twice as many as Gab's score, so Cher scored 40 x 2 = 80 points. Together, Sammy, Gab, and Cher scored 20 + 40 + 80 = 140 points. Their opponent scored 85 points. To find out how many more points they have than their opponent, we subtract their opponent's score from their total score: 140 - 85 = 55. They have 55 more points than their opponent. 55 The answer is: 55