A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 19 feet and the area of the rug is 24 square feet, how wide will the border be?
To find the width of the border, we need to subtract the dimensions of the room from the dimensions of the rug.
1. Start by finding the area of the room by multiplying its length and width:
Area of the room = Length of the room × Width of the room
Area of the room = 9 feet × 19 feet
Area of the room = 171 square feet
2. Subtract the area of the rug from the area of the room to get the total area of the border:
Total area of the border = Area of the room - Area of the rug
Total area of the border = 171 square feet - 24 square feet
Total area of the border = 147 square feet
3. Since the border is consistent on all four sides, we can assume it has the same width. Let's denote the width of the border as 'x' feet.
4. Multiply the width of the border by the combined length and width of the room to get the total area of the border:
Total area of the border = Width of the border × (Length of the room + Width of the room)
147 square feet = x feet × (9 feet + 19 feet)
147 square feet = x feet × 28 feet
5. Divide both sides of the equation by 28 feet to solve for the width of the border:
(147 square feet) / 28 feet = x feet
x = 5.25 feet
The width of the border will be 5.25 feet.