Answer:
Longer piece = 2.042 feet
Shorter piece = 1.292 feet
Step-by-step explanation:
Let L represents the longer piece of yarn and S shorter piece of yarn
The difference between longer and short piece of yarn is given as
L - S = 3/4
L = 3/4 + S eq. 1
There are 6 longer and shorter pieces of yarn totaling 20 feet of length,
6(L+S) = 20 eq. 2
Substitute eq. 1 into eq. 2
6(3/4 + S +S) = 20
6(3/4 + 2S) = 20
9/2 + 12S = 20
12S = 20 - 9/2
12S = 31/2
S = (31/2)/12
S = 31/24 feet
S = 1.292 feet
So the shorter piece is 1.292 feet long.
Substitute the value of S into eq. 1
L - 31/24 = 3/4
L = 3/4 + 31/24
L = 49/24
L = 2.042 feet
Therefore, the longer piece is 2.042 feet long.
The combined length of both pieces
L + S = 2.042 + 1.292 = 3.334 feet
There will be 6 such pieces of length 3.334 feet.
A line plot is attached which shows the length of longer and shorter pieces of yarn and also the combined length of both pieces that can be used by Maria.
