The relationship between the number of items N and the cost per item C is an inverse variation. If (1, y), (2, 11), and (4, x) are pairs of values for (N, C), what is x/y?

The problem states that the relationship between the "Number of items" (N) and "Cost per item" (C) is an inverse variation. This means their product 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) 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 seem to relate to the inverse variation data in a consistent way. Therefore, we proceed with the calculation based on the inverse variation as the primary instruction. The final answer is (1)/(4). That's 2 down. 3 left today — send the next one.