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question:An investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the capital within a year. If he invested x in scheme A and 200 in B, how much more money will he have in scheme A than in B after a year, He has 90 provided he does not withdraw anything. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the amount of money the investor invested in scheme A. Let's break down the information given: Amount of money invested in scheme A: x Amount of money invested in scheme B: 200 Yield from scheme A: 30% of the capital Yield from scheme B: 50% of the capital Total amount after a year: 90 We can set up the equation as follows: Amount of money invested in scheme A + Yield from scheme A - (Amount of money invested in scheme B + Yield from scheme B) = Total amount after a year x + 0.3x - (200 + 0.5(200)) = 90 Let's simplify and solve for x: x + 0.3x - 200 - 0.5(200) = 90 1.3x - 200 - 100 = 90 1.3x - 300 = 90 To isolate x, we add 300 to both sides of the equation: 1.3x - 300 + 300 = 90 + 300 1.3x = 390 To solve for x, we divide both sides of the equation by 1.3: x = 390 / 1.3 x = 300 The value of x is 300. 300 The answer is: 300
question:f Lassie Lake has forty-five frogs and Lake Crystal has twenty percent fewer frogs than Lassie Lake, what is the total number of frogs in the two lakes?
answer:If Lassie Lake has forty-five frogs, Lake Crystal has 20/100 * 45 = <<20/100*45=9>>9 frogs fewer than Lassie Lake. So, Lake Crystal has 45 - 9 = <<45-9=36>>36 frogs. The total number of frogs in the two lakes is 45 + 36 = <<45+36=81>>81 frogs. 81 The answer is: 81
question:f Nick wants to raise 1000 for a charity by selling candy bars for 5 each and chocolate oranges for 10 each, and he has already sold out of his 20 chocolate oranges, how many candy bars does he need to sell in order to reach his fundraising goal?
answer:Nick has already sold out of his 20 chocolate oranges, so he has already raised 20 * 10 = 200. He wants to raise a total of 1000, so he still needs to raise 1000 - 200 = 800. He sells candy bars for 5 each, so he needs to sell 800 / 5 = 160 candy bars. Therefore, Nick needs to sell 160 candy bars in order to reach his fundraising goal. 160 The answer is: 160
question:w many integers between 1 and 200 are multiples of both 3 and 5 but not of either X or 7? If we know the answer to the above question is 9, 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 integers between 1 and 200 that are multiples of both 3 and 5 but not of either X or 7, we can use the concept of the least common multiple (LCM). The LCM of two numbers is the smallest positive integer that is divisible by both numbers. In this case, the LCM of 3 and 5 is 15. So, we need to find the number of integers between 1 and 200 that are multiples of 15 but not of either X or 7. To do this, we can divide 200 by 15 to find the number of multiples of 15 between 1 and 200. This gives us 13. However, we also need to exclude the multiples of either X or 7. Given that the number of integers meeting the criteria is 9, we can subtract this from the total number of multiples of 15 to find the number of multiples of either X or 7. 13 - 9 = 4 Therefore, the value of X is 4. The answer is: 4