A 36 foot long ribbon is cut into 3 pieces the first piece of the ribbon is half as long he second piece of ribbon the third piece is 1 foot longer than twice the second piece of ribbon. how long is the longest piece?
To determine the length of the longest piece of ribbon, let's assign variables to the lengths of the three pieces. Let's say the first piece is represented by "x," the second piece by "y," and the third piece by "z."
Given the information, we know that the first piece is half as long as the second piece. Therefore, we can express this relationship as: x = (1/2)y
We are also told that the third piece is one foot longer than twice the second piece. This relationship can be expressed as: z = 2y + 1
Now let's use the information given to set up an equation relating the lengths of the three pieces. We know that the total length of the ribbon is 36 feet, so:
x + y + z = 36
Substituting the given relationships, we have:
(1/2)y + y + 2y + 1 = 36
Combining like terms, we get:
(5/2)y + 1 = 36
Subtracting 1 from both sides, we have:
(5/2)y = 35
To isolate y, we divide both sides by (5/2):
y = (35 * 2) / 5
y = 14
Now that we know the value of y, we can use the relationship x = (1/2)y to find the length of the first piece:
x = (1/2) * 14
x = 7
Lastly, we can use the relationship z = 2y + 1 to find the length of the third piece:
z = 2 * 14 + 1
z = 29
Therefore, the first piece is 7 feet long, the second piece is 14 feet long, and the longest piece (the third piece) is 29 feet long.
If the 1st piece is x, then
x + 2x + 2x+1 = 36
Now finish it off