Amber has a piece of licorie that is 10 feet long. She cuts it into three pieces for her friends. The 1st piece is 4.25 feet longer than the second piece. The 3rd piece is 2.24 feet longer than the second. How long is the 3rd piece?
let the second be x ft long
then the first is x+4.25
the third is x+2.24
x + x+4.25 + x+2.24 = 10
carry on
L1 = Length of 1st piece
L2 = Length of 2st piece
L3 = Length of 3st piece
The 1st piece is 4.25 feet longer than the second piece mean:
L1 = L2 + 4.25
The 3rd piece is 2.24 feet longer than the second mea.
L3 = L2 + 2.24
L1 + L2 + L3 = 10 ft
L2 + 4.25 + L2 + L2 + 2.24 = 10
3 L2 + 6.49 = 10 Subtract 6.49 to both sides
3 L2 + 6.49 - 6.49 = 10 - 6.49
3 L2 = 3.51 Divide both sides by 3
L2 = 3.51 / 3 = 1.17 ft
L1 = L2 + 4.25 = 1.17 + 4.25 = 5.42 ft
L3 = L2 + 2.24 = 1.17 + 2.24 = 3.41 ft
L1 = 5.42 ft , L2 = 1.17 ft , L3 = 3.41 ft
3rd piece is 3.41 ft long.
To find the length of the third piece, we need to first determine the length of the second piece. Let's assume the length of the second piece is x feet.
According to the given information, the first piece is 4.25 feet longer than the second piece. So, the length of the first piece is x + 4.25 feet.
The third piece is 2.24 feet longer than the second piece. Therefore, the length of the third piece is x + 2.24 feet.
Now, we know the sum of the lengths of all three pieces should equal 10 feet. We can express this information in an equation:
x + (x + 4.25) + (x + 2.24) = 10
Simplifying the equation:
3x + 6.49 = 10
Subtracting 6.49 from both sides:
3x = 3.51
Dividing both sides by 3:
x = 1.17
Therefore, the length of the second piece is 1.17 feet.
To find the length of the third piece, we substitute this value back into the equation:
x + 2.24 = 1.17 + 2.24 = 3.41
Hence, the length of the third piece is 3.41 feet.