Appearance
question:What is the 5th term of an arithmetic sequence of 20 terms with first and last terms of 2 and X, respectively? If we know the answer to the above question is 14, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. We are given that the arithmetic sequence has 20 terms, with the first term being 2 and the last term being X. The formula for the nth term of an arithmetic sequence is: a_n = a_1 + (n-1)d where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference. In this case, we are looking for the 5th term, so we can substitute n = 5 into the formula: a_5 = 2 + (5-1)d Simplifying, we have: a_5 = 2 + 4d Given that the value of the 5th term is 14, we can substitute it into the equation: 14 = 2 + 4d Subtracting 2 from both sides of the equation, we find: 12 = 4d Dividing both sides of the equation by 4, we get: d = 3 Now, we can substitute the value of d into the formula to find X: a_{20} = 2 + (20-1)3 a_{20} = 2 + 57 a_{20} = 59 Given that the value of the last term X is 59, we have: X = 59 The value of X is 59. The answer is: 59
question:A private company raised 2500 to be used for charity. They donated 80% to a public foundation with 8 organizations. How much money will each organization receive?
answer:The company donated 80% of 2500, which is 80/100 * 2500 = 2000. Since there are 8 organizations, each organization will receive 2000 / 8 = 250. Each organization will receive 250. 250 The answer is: 250
question:Joshua and Justin shared 40. Joshua’s share was thrice as much as Justin’s. How much is Joshua's share?
answer:Let's assume Justin's share is x dollars. Since Joshua's share is thrice as much as Justin's, Joshua's share is 3x dollars. The total amount shared is the sum of Joshua's and Justin's share, which is 3x + x = 4x dollars. We know that the total amount shared is 40, so 4x = 40. To find Joshua's share, we need to solve for x. Dividing both sides of the equation by 4, we have x = 40 / 4 = 10. Therefore, Joshua's share is 3x = 3(10) = 30. 30 The answer is: 30
question:To keep himself busy in class, Michael makes rubber-band balls. He makes two sizes, large and small. A small ball uses 50 rubber bands. A large ball requires 300 rubber bands. Michael brought a x pack to class and already made 22 small balls. He can make 13 large balls with the remaining rubber bands. 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 rubber bands in the pack that Michael brought to class. Let's break down the information given: Number of rubber bands used for a small ball: 50 Number of rubber bands used for a large ball: 300 Number of small balls made: 22 Number of large balls made: 13 We can set up the equation as follows: Number of rubber bands used for small balls + Number of rubber bands used for large balls + Remaining rubber bands = Total number of rubber bands in the pack 22 * 50 + 13 * 300 + Remaining rubber bands = x Let's simplify and solve for x: 1100 + 3900 + Remaining rubber bands = x 5000 + Remaining rubber bands = x To isolate x, we subtract 5000 from both sides of the equation: 5000 + Remaining rubber bands - 5000 = x - 5000 Remaining rubber bands = x - 5000 Since the remaining rubber bands are not specified, we cannot determine the exact value of x. The value of x could be any number greater than or equal to 5000. The value of unknown variable x is indeterminate. 5000 The answer is: 5000