answer:To solve this problem, we need to determine the value of x, which represents the number of cherry sours that Sally scooped into the bag. Let's break down the information given: Number of cherry sours: x Ratio of cherry sours to lemon sours: 4:5 Number of lemon sours: (5/4)x Number of orange sours: 25% of the total sours = 0.25 * 96 = 24 Total number of sours: Number of cherry sours + Number of lemon sours + Number of orange sours Total number of sours = x + (5/4)x + 24 We can set up the equation as follows: Total number of sours = 96 x + (5/4)x + 24 = 96 Let's simplify and solve for x: (4/4)x + (5/4)x + 24 = 96 (9/4)x + 24 = 96 To isolate x, we subtract 24 from both sides of the equation: (9/4)x + 24 - 24 = 96 - 24 (9/4)x = 72 To solve for x, we multiply both sides of the equation by 4/9: (4/9)(9/4)x = (4/9)(72) x = 32 The value of x is 32. 32 The answer is: 32

answer:If we let x be the number of lattes sold, then the coffee shop sold 4x + 8 lattes. We are given that 6 teas were sold, so the number of lattes sold is equal to 4(6) + 8 = 24 + 8 = 32. Therefore, the coffee shop sold 32 lattes. 32 The answer is: 32

answer:We can rewrite the equation as 7 = left(x + frac{1}{x}right)^2 - 2. Simplifying, we have left(x + frac{1}{x}right)^2 = 9. Taking the square root of both sides, we get x + frac{1}{x} = pm 3. The maximum value is boxed{3}.The answer is: 3

answer:We can rewrite the equation as (x-2)^2 + (y-6)^2 = 4 by completing the square. This is the equation of a circle with center (2, 6) and radius 2. Therefore, the sum of h and k is 2 + 6 = boxed{8}.The answer is: 8