the cost of an antique plate varies directly with its area. if an antique plate with an area of 148 square…

the cost of an antique plate varies directly with its area. if an antique plate with an area of 148 square inches costs $8, how much, in dollars, should an antique plate with an area of 147 square inches cost? provide an answer accurate to the nearest hundredth.

the cost of an antique plate varies directly with its area. if an antique plate with an area of 148 square inches costs $8, how much, in dollars, should an antique plate with an area of 147 square inches cost? provide an answer accurate to the nearest hundredth.

Answer

Explanation:

Step1: Find the constant of variation

Since cost $C$ varies directly with area $A$, we have $C = kA$. Given $A = 148$ square - inches and $C = 8$, we can find $k$ by substituting these values into the equation: $k=\frac{C}{A}=\frac{8}{148}=\frac{2}{37}$.

Step2: Calculate the cost for the new area

We want to find the cost $C$ when $A = 147$ square - inches. Using the equation $C = kA$ and $k=\frac{2}{37}$, we substitute $A = 147$ into the equation: $C=\frac{2}{37}\times147=\frac{294}{37}\approx7.95$.

Answer:

$7.95$