SOLUTION: Crown molding is a decorative trim installed over the joint between the walls of a room and the ceiling. (If you are not sure that you understand the idea, do an Internet search to
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Question 1128349: Crown molding is a decorative trim installed over the joint between the walls of a room and the ceiling. (If you are not sure that you understand the idea, do an Internet search to find an example picture of crown molding). Andy intends to install crown molding around the four sides of the dining room. There will be no gaps. The dining room ceiling is a rectangle with dimensions 16 feet 9 inches by 13 feet. The crown molding is sold in 8-foot lengths that cost $24 each. He decides to purchase enough pieces to allow for 10% waste due to possible mistakes.
1.What is the perimeter of the dining room in feet and inches?
2.How many 8-foot boards are needed?
3.If sales tax is 8.25%, what is the total cost?
THANK YOU!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Problem 1
Add up the length and width of the dining room:
(Length) + (Width) = (16 ft, 9 in) + (13 ft, 0 in)
(Length) + (Width) = (16 ft+13 ft) + (9in + 0 in)
(Length) + (Width) = 29 ft, 9 in
Now double this result to get the perimeter
perimeter = 2*(length + width)
perimeter = 2*(29 ft, 9 in)
perimeter = 2*(29 ft+9 in)
perimeter = 2*(29 ft)+2*(9 in)
perimeter = 58 ft + 18 in
perimeter = 58 ft + 12 in + 6 in
perimeter = 58 ft + 1 ft + 6 in
perimeter = 59 ft + 6 in
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Answer: 59 ft, 6 in
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Problem 2
If there is 0% waste, then every bit of board is used to create the 59 ft, 6 in perimeter.
If there is 10% waste, then 90% is used to make the 59 ft, 6 in perimeter and the other 10% is garbage
If x is the total amount of wood in feet, then
90% of x = perimeter
0.90*x = 59 ft, 6 in
0.90*x = 59 ft+6 in
0.90*x = 59 ft+6/12 ft
0.90*x = 59 ft+0.5 ft
0.90*x = 59.05 ft
0.90*x = 59.05
x = 59.05/0.90
x = 65.611
This means that he desires about 65.611 ft of molding.
Divide this over 8 to get
65.611/8 = 8.201375
which rounds up to 9.
We round up instead of round down to make sure we hit the goal. We'll have leftover wood that isn't lost to waste and that isn't used to make the molding.
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Answer: 9
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Problem 3
Each board is $24, and we need 9 boards, so 9*24 = 216 is the total cost before tax is applied.
Apply the 8.25% tax to get
0.0825*216 = 17.82, so we pay $17.82 in tax
The total cost after tax is 216+17.82 = 233.82
A shortcut is to compute
1.0825*216 = 233.82
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Answer: 233.82
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