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question:Myrtle’s 3 hens lay 3 eggs a day. She would be gone for x days and told her neighbor to take as many as they would like. The neighbor took 12 eggs. Once home, Myrtle collected the remaining eggs, dropping 5 on the way into her house. Myrtle has 46 eggs. What is the value of unknown variable x? 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 days Myrtle was gone. Let's break down the information given: Number of hens: 3 Number of eggs laid by each hen per day: 3 Number of eggs taken by the neighbor: 12 Number of eggs dropped by Myrtle: 5 Total number of eggs Myrtle has: 46 We can set up the equation as follows: (Number of hens * Number of eggs laid per day * Number of days) - Number of eggs taken by the neighbor - Number of eggs dropped by Myrtle = Total number of eggs Myrtle has (3 * 3 * x) - 12 - 5 = 46 Let's simplify and solve for x: 9x - 12 - 5 = 46 9x - 17 = 46 To isolate x, we add 17 to both sides of the equation: 9x - 17 + 17 = 46 + 17 9x = 63 To solve for x, we divide both sides of the equation by 9: x = 63 / 9 x = 7 The value of x is 7. 7 The answer is: 7
question:Thomas has 25 drawings to display. 14 of the drawings were made using colored pencils. x of the drawings were made using blending markers. The rest of the drawings were made with charcoal. There are 4 charcoal drawings. 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 drawings made using blending markers. Let's break down the information given: Number of drawings made using colored pencils: 14 Number of charcoal drawings: 4 Total number of drawings: 25 We can set up the equation as follows: Number of drawings made using colored pencils + Number of drawings made using blending markers + Number of charcoal drawings = Total number of drawings 14 + x + 4 = 25 Let's simplify and solve for x: 18 + x = 25 To isolate x, we subtract 18 from both sides of the equation: 18 + x - 18 = 25 - 18 x = 7 The value of x is 7. 7 The answer is: 7
question:After buying shirts worth 27 from a store, Dennis received x 10 bills and 3 in loose coins for his change. Dennis initially had 50 money. What is the value of unknown variable x? 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 10 bills Dennis received as change. Let's break down the information given: Cost of the shirts: 27 Amount of change received in 10 bills: x Amount of change received in loose coins: 3 Initial amount of money: 50 We can set up the equation as follows: Initial amount of money - Cost of the shirts - Amount of change received in loose coins - Amount of change received in 10 bills = 0 50 - 27 - 3 - 10x = 0 Let's simplify and solve for x: 50 - 27 - 3 - 10x = 0 20 - 10x = 0 To isolate x, we subtract 20 from both sides of the equation: 20 - 20 - 10x = 0 - 20 -10x = -20 To solve for x, we divide both sides of the equation by -10: x = -20 / -10 x = 2 The value of x is 2. 2 The answer is: 2
question:A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. For example, June 17 is a relatively prime date because the greatest common factor of 6 and 17 is X. There are 10 relatively prime dates in the month with the fewest relatively prime dates. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the greatest common factor of the number of the month and the number of the day for a relatively prime date. We know that there are 10 relatively prime dates in the month with the fewest relatively prime dates. The month with the fewest relatively prime dates is February, which has 28 days. Therefore, we need to find the value of x such that there are 10 relatively prime dates in the month of February. To do this, we can list out the possible pairs of numbers for the month and the day, and check if their greatest common factor is equal to x. The possible pairs of numbers for the month and the day are (1, 1), (1, 3), (1, 5), ..., (2, 1), (2, 3), ..., (28, 27), (28, 29). Out of these pairs, we need to find the ones for which the greatest common factor is equal to x. Since there are 10 relatively prime dates, we can assume that x is a prime number, as the greatest common factor of two numbers is always a factor of both numbers. Looking at the pairs of numbers, we can see that the greatest common factor of each pair is 1, except for the pairs (1, 2), (1, 4), (1, 6), ..., (1, 28), (2, 2), (2, 4), ..., (28, 28). Therefore, the value of x is 1. The value of x is 1. The answer is: 1