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question:Peggy is moving and is looking to get rid of her record collection. Sammy says that he will buy all of them for 4 dollars each. Bryan is only interested in half of the records but will offer 6 dollars each for the half that he is interested in and 1 dollar each for the remaining half that he is not interested in with the hopes that he can resell them in bulk later. If Peggy has x records, The difference in profit between Sammy versus Bryan's deal is 100. 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 records Peggy has. Let's break down the information given: Sammy's offer: 4 per record Bryan's offer for the records he is interested in: 6 per record Bryan's offer for the remaining records: 1 per record Difference in profit between Sammy and Bryan's deal: 100 We can set up the equation as follows: Total profit from Sammy's deal - Total profit from Bryan's deal = Difference in profit (x * 4) - (x/2 * 6 + x/2 * 1) = 100 Let's simplify and solve for x: 4x - (3x + x/2) = 100 4x - (6x/2 + x/2) = 100 4x - 7x/2 = 100 To combine like terms, we multiply 4x by 2/2: (8x - 7x)/2 = 100 x/2 = 100 To isolate x, we multiply both sides of the equation by 2: (x/2) * 2 = 100 * 2 x = 200 The value of x is 200. 200 The answer is: 200
question:Sarah is buying Christmas presents for her family. She starts her shopping with a certain amount of money. She buys 2 toy cars for 11 each for her sons. She buys a scarf for 10 for her mother. Then she buys a beanie for 14 for her brother. If she has 7 remaining after purchasing the beanie, how much money did she start with?
answer:Sarah buys 2 toy cars for 11 each, so she spends 2 * 11 = 22 on the toy cars. She also buys a scarf for 10 and a beanie for 14, so she spends 10 + 14 = 24 on the scarf and beanie. After purchasing the beanie, she has 7 remaining, so she spent 24 + 7 = 31 in total. Therefore, Sarah started with 31 + 22 = 53. 53 The answer is: 53
question:Louise is in a toy store. She already has 28 toys worth 10 each in her cart. On her way to the till she adds 20 teddy bears to the cart. If the 580 in Louise’s wallet is exactly enough to pay for all the toys, how much does each teddy bear cost?
answer:Louise already has 28 toys worth 10 each in her cart, so the total cost of those toys is 28 * 10 = 280. She adds 20 teddy bears to the cart, so the total cost of the teddy bears is 580 - 280 = 300. To find the cost of each teddy bear, we divide the total cost of the teddy bears by the number of teddy bears: 300 / 20 = 15. Therefore, each teddy bear costs 15. 15 The answer is: 15
question:What is the smallest possible value of x such that 2x^2+24x-60=x(x+13)?
answer:Expanding the right side, we have 2x^2+24x-60=x^2+13x. Subtracting x^2+13x from both sides, we have x^2+11x-60=0. Factoring the quadratic, we have (x-4)(x+15)=0. Setting each factor equal to 0, we have x-4=0 or x+15=0. Solving each equation, we find x=4 or x=-15. Since we are looking for the smallest possible value, the answer is boxed{-15}. The answer is: -15