Gary makes custom metal signs. He has a sheet of metal that is 6 feet by 12 feet and wants to cut it into signs that are 2 feet by 4 feet. How many signs can he make?
6 = 2*3
12 = 4*3
6*12 = (2*3)(4*3)/(2*4) = 3*3 = 9
To find out how many signs Gary can make, we need to determine the number of signs that can fit on the sheet of metal.
First, let's calculate the area of the sheet of metal. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 6 feet and the width is 12 feet, so the area of the sheet is:
Area of sheet = Length × Width = 6 feet × 12 feet = 72 square feet.
Next, let's calculate the area of each sign. Each sign has a length of 2 feet and a width of 4 feet, so the area of each sign is:
Area of sign = Length × Width = 2 feet × 4 feet = 8 square feet.
To determine the number of signs Gary can make, we need to divide the area of the sheet by the area of each sign:
Number of signs = Area of sheet ÷ Area of sign = 72 square feet ÷ 8 square feet = 9 signs.
Therefore, Gary can make 9 signs from the sheet of metal.