Vincent has cut three pieces of rope to complete a science project. Two pieces are of equal length. The third piece is one-quarter the length of each rope of the others. He cut the three pieces from a rope 54 meters long with any rope left over. Fine the answer of meters in each piece. [Show or explain the procedure used to obtain the answer.]
Let L be the length of the two long ropes. The third rope has length L/4
The total length of all three ropes is
2 1/4 L = 9L/4 and that equals 54 m
If 9L/4 = 54, then
L/4 = 6 m
One more step.
Let x be the length of the first two ropes and 1/2 x be the length of the third rope (Because the problem says that the 3rd rope is 1/4 the length of EACH of the other ropes. So we add, 1/4 + 1/4= 2/4 or 1/2)
x+x+1/2x= 54
2 1/2x=54 or 5/2x=54
x= 54 multiplied by 2/5 (Transposition)
x= 21 3/5 or 21.6
If we substitute this, then the values will be
21.6, 21.6 and 10.8
If you add those you will get 54
To find the length of each piece, we'll use algebraic equations.
Let's assume the length of the two equal pieces is 'x' meters.
So, the length of the third piece is (1/4)x meters.
Given that the total length of the rope is 54 meters, we can create an equation:
x + x + (1/4)x = 54
Combining like terms, we get:
(2 + 1/4)x = 54
To remove the fraction, let's multiply both sides of the equation by 4:
4(2 + 1/4)x = 4(54)
8 + x = 216
Now, subtract 8 from both sides:
x = 216 - 8
x = 208
So, the length of each of the two equal pieces is 208 meters.
Now, let's find the length of the third piece:
(1/4)x = (1/4)(208) = 52
Therefore, the length of each piece is as follows:
- The two equal pieces are 208 meters each.
- The third piece is 52 meters.