answer:To solve this problem, we need to determine the value of x, which represents the number of diamond earrings in the Oscar swag bags. Let's break down the information given: Cost of each diamond earring: 6,000 Cost of the new iPhone: 2,000 Number of designer scarves: 4 Cost of each scarf: 1,500 Total value of the swag bag: 20,000 We can set up the equation as follows: Number of diamond earrings * Cost per earring + Cost of the new iPhone + (Number of scarves * Cost per scarf) = Total value of the swag bag x * 6,000 + 2,000 + (4 * 1,500) = 20,000 Let's simplify and solve for x: 6,000x + 2,000 + 6,000 = 20,000 6,000x + 8,000 = 20,000 To isolate x, we subtract 8,000 from both sides of the equation: 6,000x + 8,000 - 8,000 = 20,000 - 8,000 6,000x = 12,000 To solve for x, we divide both sides of the equation by 6,000: x = 12,000 / 6,000 x = 2 The value of x is 2. 2 The answer is: 2

answer:We want to find the value of X in the given situation. We are given that two positive integers differ by X and their product is 135. Let's call the larger integer a and the smaller integer b. According to the given information, we can set up two equations: a - b = X (Equation 1) a * b = 135 (Equation 2) To find the larger integer, which is a, we can solve this system of equations. We can rewrite Equation 2 as: b = frac{135}{a} Substituting this into Equation 1, we have: a - frac{135}{a} = X Multiplying both sides of the equation by a to eliminate the fraction, we get: a^2 - 135 = Xa Rearranging the equation, we have: a^2 - Xa - 135 = 0 Now, we can use the quadratic formula to solve for a: a = frac{-(-X) pm sqrt{(-X)^2 - 4(1)(-135)}}{2(1)} Simplifying this equation, we have: a = frac{X pm sqrt{X^2 + 540}}{2} Given that the value of the larger integer a is 15, we can substitute it into the equation: 15 = frac{X pm sqrt{X^2 + 540}}{2} Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 30 = X pm sqrt{X^2 + 540} Subtracting sqrt{X^2 + 540} from both sides of the equation, we find: 30 - sqrt{X^2 + 540} = X To find the value of X, we can square both sides of the equation: (30 - sqrt{X^2 + 540})^2 = X^2 Expanding the equation, we have: 900 - 60sqrt{X^2 + 540} + X^2 + 540 = X^2 Simplifying, we get: 1440 - 60sqrt{X^2 + 540} = 0 Dividing both sides of the equation by 60, we find: 24 - sqrt{X^2 + 540} = 0 Adding sqrt{X^2 + 540} to both sides of the equation, we get: 24 = sqrt{X^2 + 540} Squaring both sides of the equation, we have: 576 = X^2 + 540 Subtracting 540 from both sides of the equation, we find: 36 = X^2 Taking the square root of both sides of the equation, we get: X = pm 6 Given that X is a positive value, we can disregard the negative solution. The value of X is 6. The answer is: 6

answer:Nathan bought one large box of bananas. He saw that there are six bunches with x bananas in a bunch, which means there are 6x bananas in total from these bunches. He also saw that there are five bunches with seven bananas in a bunch, which means there are 5 * 7 = 35 bananas in total from these bunches. The total number of bananas Nathan has is the sum of the bananas from the bunches with x bananas and the bananas from the bunches with seven bananas: 6x + 35. We are given that the total number of bananas is 83, so we can write: 6x + 35 = 83. Solving for x, we get: 6x = 48. Dividing both sides by 6, we get: x = 8. The value of x is 8. 8 The answer is: 8

answer:If one-sixth of the pea patch is equal to 5 square feet, then the total size of the pea patch is 5 * 6 = 30 square feet. Since the pea patch is twice as big as the radish patch, the radish patch is 30 / 2 = 15 square feet. 15 The answer is: 15