Question

The cost of an antique plate varies directly with its area. If an antique plate with an area of 185 square inches costs $14, how much, in dollars, should an antique plate with an area of 295 square inches cost? Round your answer to the nearest hundredth. Label Required.

Answer 1

To find the cost of an antique plate with a given area, we need to use the direct variation formula. Substitute the given values into the formula to find the constant of variation. Use the constant of variation to calculate the cost of an antique plate with a different area.

Step-by-step explanation:

To find the cost of an antique plate with a given area, we need to use the direct variation formula.

The formula for direct variation is: y = kx, where y is the cost, x is the area, and k is the constant of variation.

To find the value of k, we can substitute the given values for the cost and area into the formula:

14 = k * 185

Solving for k, we get k = 14 / 185 = 0.0757.

Now, we can use the value of k to find the cost of an antique plate with an area of 295 square inches:

cost = k * area = 0.0757 * 295 = 22.33.

Therefore, an antique plate with an area of 295 square inches should cost $22.33.