A bolt of cloth 100 yards long is cut into three pieces. The second piece is 15 yards longer than the first piece, and the length of the third piece is 5 yard more than twice the length of the first piece.
x = first piece
x+15 = second piece
2x+5 = third piece
x + (x+15) + (2x+5) = 100
Solve for x, then others.
To find the lengths of the three pieces, let's assign variables to represent their lengths.
Let's call the length of the first piece "x" yards.
Since the second piece is 15 yards longer than the first piece, its length would be "x + 15" yards.
And since the third piece is 5 yards more than twice the length of the first piece, its length would be "2x + 5" yards.
Now, we need to create an equation using the information given. The sum of the lengths of the three pieces equals the total length of the cloth, which is 100 yards.
So, the equation would be:
x + (x + 15) + (2x + 5) = 100
Now, we can solve this equation to find the value of "x" and then determine the lengths of the three pieces.
Combining like terms, we have:
4x + 20 = 100
Subtracting 20 from both sides, we get:
4x = 80
Dividing both sides by 4, we find:
x = 20
Therefore, the length of the first piece is 20 yards.
Substituting this value back into our expressions,
the second piece is 20 + 15 = 35 yards,
and the third piece is 2(20) + 5 = 45 yards.
So, the lengths of the three pieces are:
First piece: 20 yards
Second piece: 35 yards
Third piece: 45 yards