Question

Crown molding is a decorative trim installed over the joint between the walls of a roomand the ceiling. (If you are not sure that you understand the idea, do an Internet searchto find an example picture of crown molding). Andy intends to install crown moldingaround the four sides of the dining room. There will be no gaps. The dining room ceilingis a rectangle with dimensions 10 feet 10 inches by 9 feet. The crown molding is sold in8-foot lengths that cost $22 each. He decides to purchase enough pieces to allow for10% waste due to possible mistakes.Submit answerExit

Answer 1

Since the crown molding will be installed around the ceiling with no gaps, we need to calculate the perimeter of the room, which is the sum of all its sides.

This is done below:

`\begin{gathered} P=2\cdot(10.833+9) \\ P=39.67\text{ feet } \end{gathered}`

Since he wants to buy 10% extra, we need to multiply the perimeter by 1.1.

`\text{ Material to buy}=39.67\cdot1.1=43.64`

He needs 43.64 feet or 43 feet 8 inches.

`\begin{gathered} \text{wood}=(43.64)/(8) \\ \text{wood}=5.83 \end{gathered}`

He needs 6 pieces of wood.

To determine the price with the tax, we need to first determine the price without it. For that we have to multiply the number of pieces of wood by the cost of each wood.

`\begin{gathered} \text{ cost before tax}=6\cdot22 \\ \text{ cost before tax}=132 \end{gathered}`

Now we have to multiply the cost before tax by the value of the tax and add the result to the cost before tax.

`\begin{gathered} \text{total cost}=132\cdot(8.25)/(100)+132 \\ \text{total cost}=132\cdot0.0825+132 \\ \text{total cost}=10.89+132 \\ \text{total cost}=142.89 \end{gathered}`

The cost with tax is 142.89