A roll of fabric is 12 yards long. A salesperson cuts three pieces off the roll measuring 2 3/4 yd, 5 1/3 yd, and 1 1/5 yd. Approximately what percentage of the roll of fabric remains?
A
3%
B
9%
C
23%
D
77%
To find the remaining percentage of the roll of fabric, we need to subtract the total length of the three pieces that were cut from the original length of the roll and then find what percentage that remaining length represents.
The total length of the three pieces that were cut is:
2 3/4 yd + 5 1/3 yd + 1 1/5 yd = (11/4) yd + (16/3) yd + (6/5) yd
= (165/60) yd + (320/60) yd + (72/60) yd
= (557/60) yd
Now, we subtract this total length from the original length of the roll, which is 12 yards:
12 yd - (557/60) yd = (720/60) yd - (557/60) yd
= (163/60) yd
To find the percentage, we divide the remaining length by the original length and multiply by 100:
[(163/60) yd / (12 yd)] * 100 = (163/720) * 100
≈ 22.6389 %
Rounded to the nearest whole number, approximately 23% of the roll of fabric remains.
Therefore, the correct answer is C: 23%.
To find the percentage of fabric remaining, we need to calculate the total length of the fabric that was cut off, and then subtract it from the total length of the roll.
First, let's convert all the measurements to the same format.
2 3/4 yd can be written as (2 + 3/4) yd = 11/4 yd
5 1/3 yd can be written as (5 + 1/3) yd = 16/3 yd
1 1/5 yd can be written as (1 + 1/5) yd = 6/5 yd
Now, we can add up these measurements:
11/4 yd + 16/3 yd + 6/5 yd
To add fractions, we need to find a common denominator. The least common multiple of 4, 3, and 5 is 60.
So, let's convert these fractions to have 60 as the denominator:
(11/4) * (15/15) = 165/60 yd
(16/3) * (20/20) = 320/60 yd
(6/5) * (12/12) = 72/60 yd
Now we can add them together:
165/60 yd + 320/60 yd + 72/60 yd = 557/60 yd
Next, we subtract this from the total length of the roll, which is 12 yd:
12 yd - 557/60 yd
To subtract fractions, we need a common denominator:
12 yd * (60/60) = 720/60 yd
(720/60 yd) - (557/60 yd) = 163/60 yd
To find the percentage remaining, we need to divide the remaining fabric by the original length and multiply by 100:
(163/60 yd) / (720/60 yd) * 100 = (163/720) * 100
Now, we can calculate this fraction:
163/720 = 0.22638
To express this as a percentage, we multiply by 100:
0.22638 * 100 = 22.638
Rounded to the nearest whole number, approximately 22.638% of the roll of fabric remains.
Therefore, the answer is C. 23%
3%
Who ever put 77% is dumb
12 - 2.75 - 5.333 - 1.2 = 2.72
100 (2.72/12 = _______%