A rope is cut in half and one half is used.Then one fifth of the remaining rope is cut off and used for another purpose.the piece of the rope left is 12 meters long.How long was the rope originally?
1/2 * 1/5 = 1/10
so, that leaves only 2/5 of the rope
2/5 x = 12
x = 30 meters
Let's use x to represent the original length of the rope.
After cutting it in half, one half of the rope is used, which leaves us with x/2 meters of rope.
Then, one-fifth of the remaining rope is cut off and used, which is (1/5)*(x/2) = x/10 meters.
The piece of rope left is 12 meters long, so we can set up the equation:
x/2 - x/10 = 12
To solve for x, we can first find a common denominator, which is 10:
5x/10 - x/10 = 12
Combining like terms:
(5x - x)/10 = 12
4x/10 = 12
Now, we can simplify the equation:
4x = 120
Divide both sides by 4:
x = 120/4
x = 30
Therefore, the original length of the rope was 30 meters.
To find the original length of the rope, we need to follow the steps given in the problem.
Step 1: A rope is cut in half, so the length of the remaining rope is now half of the original length.
Let's say the original length of the rope is 'x' meters.
After cutting it in half, the remaining length is (1/2)x meters.
Step 2: One-fifth of the remaining rope is cut off, so we need to find (1/5) of (1/2)x.
To find (1/5) of a number, we multiply the number by (1/5).
So, (1/5) of (1/2)x = (1/5) * (1/2)x = (1/10)x meters.
Step 3: The piece of rope left is 12 meters long.
From the problem, we know that the remaining length is 12 meters, which is equal to (1/2)x - (1/10)x.
Now we can solve for x:
(1/2)x - (1/10)x = 12
Multiply the equation by 10 to eliminate the fractions:
5x - x = 120
4x = 120
x = 120 / 4
x = 30
Therefore, the original length of the rope was 30 meters.