Complete Question:
To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².
Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?
Answer:
To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more
Explanation:
Mass of burlap sacks that Maryann collects = 6 kg
Area density of burlap = 0.4 kg/m²
Area Density = Mass / Area........(1)
The Area of bulletin board that can be made with the 6 kg of burlap sand can be calculated by using equation (1)
0.4 = 6 / Area
Area = 6/0.4
Area of bulletin board that can be made from 6 kg= 15 m² of bulletin board
The area of bulletin board that Maryann made for herself = 2 * 3 = 6m²
To make similar bulletin boards for her four friends, the total area of bulletin board made for her 4 friends = 6 * 4 = 24m²
To calculate the mass of burlap required to make a 24m² bulletin board, use equation (1)
0.4 = Mass / 24
Mass = 0.4 * 24
Mass = 9.6 kg
The mass of burlap used to make Maryann's bulletin board alone:
0.4 = Mass/6
Mass = 2.4 kg
Out of the 6kg that she got, she has used 2.4 kg for herself
The remaining mass of burlap = 6 - 2.4 = 3.6 kg
Therefore, to complete the bulletin board for her friend, she should collect (9.6 - 3.6) = 6 kg of bulletin more