MATH SOLVE

5 months ago

Q:
# Kamila has a rectangular lawn that measures 80 by 150 feet. She wants to lay gravel made from colored rock in a border, 6 feet wide, all around the lawn.Create a diagram that shows Kamila’s rectangular lawn and the gravel border. Assign variables to any unknown sides and label the diagram.Use your diagram to determine how many square feet of the gravel border will surround the lawn.Kamila decided that the depth of the gravel needs to be 2 inches. What is the total volume of gravel needed for the border? (Hint: dimensions must be in terms of the same unit before you can calculate the volume)D. A large bag of colored rock contains a cubic yard and costs $30. What is the total cost of the rocks needed for the border? (Hint: the volume of the border must be in terms of a cubic yard before you can calculate the cost)In your final answers, include all formulas, equations, and calculations necessary to determine the correct answers.

Accepted Solution

A:

ANSWER:First we need to get the dimensions of the gravel area to find the total area of the gravel.To do this, we will take the area of the lawn (gravel outside edge) and subtract the area of the uncovered lawn (inside edge).The inside edge is 6 feet in on EVERY side: top, bottom, left, and right. This shortens the length and width of the outside edge by 12 feet. 6 feet from the top + 6 feet from the bottom; 6 feet from the left + 6 feet from the right.The inside edge is 80 - 12 (58) feet long and 150 - 12 (138) feet wide.The area of the lawn is 80 * 150 (12,000) square feet. The area of the uncovered lawn is 58 * 138 (8,004) square feet. The area of the graveled lawn is: the area of the lawn without (minus) the area of the uncovered lawn.12,000 square feet - 8,004 square feet3,996 square feet.The border of gravel covers 3,996 square feet.The volume of the gravel needed is the depth of the gravel times the area of the gravel.First we need to change the unit of measurement into the same type of unit: feet.12 inches = 1 foot2 inches = 1/6 of a foot.Then, we are able to find the volume of the gravel. 3,996 square feet × 1/6 of a foot3,996/6 666 feet cubed.The volume of the gravel is 666 cubic feet.Finally, we need to determine how much buying all of these rocks will cost.First we need to know how many bags of gravel we will need to buy.1 bag = 1 yard cubed of gravel.We need to have the same unit of measurement, so we need to change one of them.1 yard = 3 feetYard × Yard × Yard = Cubic yard,3 ft × 3 ft × 3 ft = 27 cubic feet. 27 cubic feet = 1 cubic yard.1 bag of gravel is 27 cubic feet of gravel.We have 666 cubic feet of gravel, so we have 666 / 27 (24 and 2/3) bags. We cannot have only 2/3 of a bag, and we do not want to have 2/3 of a bag too little, so we will buy one full bag and only use 2/3 of that bag to get the rest of what we need. We need to buy 25 bags of gravel.Each bag of gravel costs $30.1 bag = $30, so 25 bags = $750. 25 bags × ($30 EACH bag) $750.The total cost of the rocks needed for the border is $750. So, the answers are: The border of gravel covers 3,996 square feet. The volume of the gravel is 666 cubic feet. The total cost of the rocks needed for the border is $750.