There are three pieces of rope with the lengths 15 1/3feet, 20 1/2 feet, and 30 3/4 feet.
A) how many yards in all?
B) If thery were all cut into 3 feet pieces how many would you get and how did you determine this answer
C) How much rope is left? How was that determined
I di try and answer them on my own and got A) 22 7/36 yards of rope.
B) 22 pieces
C) 7/12 of the rope was left.
Please help, are these correct?
If not can you explain and help me understand the question. Thanks
a) correct
b)
from the 15 1/3 ft piece we can cut 5 pieces of 3 ft, leaving 1/3 ft
from the 20 1/2 ft piece we can cut 6 pieces of 3 ft, leaving 2 1/2 ft
from the 30 3/4 ft piece we can cut 10 pieces of 3 ft leaving 3/4 ft
so we can cut 5+6+10 or 21 pieces of 3 ft each
c) amount left over:
1/3 + 2 1/2 + 3/4
= 3 7/12 ft
for partB) since for each part that was left was more than 3 feet as you see in part C won't that be added as one more foot making the answer to B) 22 pieces
and part C) 7/12 left?
I read the question to mean that you want complete 3 ft sections, not pieces that have been tied together to make 3 ft.
from a piece of 20 1/4 ft, I can only get 6 sections of 3 ft, even though a big piece would be left over.
Let's agree it is a poorly worded question.
A) To find the total length in yards, we need to convert the lengths of the ropes from feet to yards. There are 3 feet in 1 yard.
To convert the first rope length, 15 1/3 feet, we need to divide it by 3 to get the number of yards:
15 1/3 feet ÷ 3 = 46/3 ÷ 3 = 46/9 yards
To convert the second rope length, 20 1/2 feet, we divide it by 3:
20 1/2 feet ÷ 3 = 41/2 ÷ 3 = 41/6 yards
To convert the third rope length, 30 3/4 feet, we divide it by 3:
30 3/4 feet ÷ 3 = 123/4 ÷ 3 = 123/12 yards
Now, we add up the converted lengths in yards:
46/9 + 41/6 + 123/12 = (736 + 246 + 123) / 36 = 1105/36 yards
So, the total length of the ropes in yards is 1105/36 yards.
B) To find out how many 3 feet pieces we would get if all the ropes were cut into 3 feet pieces, we need to divide each rope length by 3.
For the first rope:
15 1/3 feet ÷ 3 feet = 46/3 ÷ 3 = 46/9 pieces
For the second rope:
20 1/2 feet ÷ 3 feet = 41/2 ÷ 3 = 41/6 pieces
For the third rope:
30 3/4 feet ÷ 3 feet = 123/4 ÷ 3 = 123/12 pieces
To determine the total number of 3 feet pieces, we add up the results:
46/9 + 41/6 + 123/12 = (736 + 246 + 123) / (9 * 2 * 2) = 1105/36 = 30 5/36 pieces
So, if all the ropes were cut into 3 feet pieces, you would get 30 5/36 pieces.
C) To find out how much rope is left, we need to subtract the total length of the 3 feet pieces from the original total length of the ropes.
Total length of the ropes = 15 1/3 feet + 20 1/2 feet + 30 3/4 feet
We already know that the total length in yards is 1105/36 yards, which we calculated in part A.
Now, we need to convert this total length back to feet:
1105/36 yards × 3 feet/1 yard = 3315/36 feet
Next, we need to subtract the length of the 3 feet pieces (30 5/36 pieces) from the total length:
3315/36 feet - 30 5/36 * 3 feet = 3315/36 feet - 95/12 feet
To subtract fractions with different denominators, we need to find a common denominator:
(3315 - 285) / 36 feet = 3030/36 feet
Simplifying the fraction:
3030/36 feet = 3030 ÷ 6 feet ÷ 6 = 505/6 feet
Therefore, the amount of rope left is 505/6 feet.