This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The problem describes an inverse variation between the "Number of items" (N) and the "Cost per item" (C). For an inverse variation, the product of the two quantities is a constant, k. N · C = k From the table, we have the following pairs of (N, C) values: 1. (1, y) 2. (2, 11) (The number of items in the second column is faintly visible as 2) 3. (4, x) Step 1: Determine the constant of variation, k. We use the complete pair (N, C) = (2, 11) to find k: k = 2 × 11 k = 22 Step 2: Find the value of y. Using the pair (N, C) = (1, y) and the constant k=22: 1 × y = 22 y = 22 Step 3: Find the value of x. Using the pair (N, C) = (4, x) and the constant k=22: 4 × x = 22 x = (22)/(4) x = (11)/(2) Step 4: Calculate (x)/(y). Now we substitute the values of x and y into the expression (x)/(y): (x)/(y) = (11)/(2)22 To simplify, we multiply the numerator by the reciprocal of the denominator: (x)/(y) = (11)/(2) × (1)/(22) (x)/(y) = (11)/(44) (x)/(y) = (1)/(4) The phrase "if the mean number is 2/6" is ambiguous and does not consistently apply to the given data under the inverse variation assumption. Therefore, the calculation is based on the inverse variation as the primary instruction. The final answer is (1)/(4). 2 done, 3 left today. You're making progress.