SOLUTION: A fabric store worker has a 57 yard bolt of cloth which is to be cut into three lengths. The length of the second piece is 5 yards shorter than twice the length of the first. The

Question 104013: A fabric store worker has a 57 yard bolt of cloth which is to be cut into three lengths. The length of the second piece is 5 yards shorter than twice the length of the first. The length of the third piece is 2 yards longer than twice the length of the second. Find the length of each piece.
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
lets call the length of the first piece x
Given: the length of the second piece is 5 yards shorter than twice the length of the first.
Now write an expression to describe the second piece in terms of x
remember the length of the first piece is x
length of the second piece = 2x-5
Ok now lets look at the third piece
Given: the length of the third piece is 2 yards longer than twice the length of the second.
Now since we have just shown that the second piece is 2x-5 we can use that to write and expression that describes the length of the third piece.
length of the third piece = 2(2x-5)+2
Ok lets look at what we have so far:
length of first = x
length of second = 2x-5
length of third = 2(2x-5)+2
Now we are also given: A fabric store worker has a 57 yard bolt of cloth
So this tell us that all three lengths of cloth add up to 57 yards
Now we can write and equation to solve for x
(x) + (2x-5) + (2(2x-5)+2) = 57
(x) + (2x-5) + (4x-10+2) = 57
x + 2x - 5 + 4x - 10 + 2 = 57
7x - 13 = 57
7x = 57 + 13
7x = 70
x = 10
The length of the first piece is 10 yards.
use this to find the lengths of the other pieces
length of second = 2x-5
length of second = 2(10)-5
length of second = 20-5
length of second = 15
The length of the second piece is 15 yards.
length of third = 2(2x-5)+2
length of third = 2(2(10)-5)+2
length of third = 2(20-5)+2
length of third = 2(15)+2
length of third = 30+2
length of third = 32
The length of the third piece is 32 yards.
Check answers
The three pieces of cloth should add up to 57 yards
10 + 15 + 32 = 57
57 = 57

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