A 143m wire is cut into three pieces. The second is 3m longer than the first. The third is 4/5 as long as the first. How long is each piece?
Let x = the first piece
x + x + 3 + 0.8x = 143
2.8x + 3 = 143
2.8x = 140
x = 50 meters
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To solve this problem, we can assign variables to represent the lengths of the three pieces of wire.
Let's say the length of the first piece is x meters.
According to the problem, the second piece is 3 meters longer than the first, so its length would be x + 3 meters.
The third piece is described as being 4/5 as long as the first piece. So, its length can be represented as 4/5x meters.
Since the total length of the wire is 143 meters, we can now form an equation based on the given information:
x + (x + 3) + (4/5)x = 143
To solve this equation, we'll simplify it:
x + x + 3 + (4/5)x = 143
(9/5)x + 3 = 143
Next, we'll isolate the variable by subtracting 3 from both sides of the equation:
(9/5)x = 143 - 3
(9/5)x = 140
To eliminate the fraction, we'll multiply both sides of the equation by 5:
5 * (9/5)x = 5 * 140
9x = 700
Finally, we'll solve for x by dividing both sides by 9:
(9x) / 9 = 700 / 9
x = 77.78
So, the length of the first piece is approximately 77.78 meters.
To find the lengths of the second and third pieces, we can substitute the value of x back into the expressions we established earlier:
Second piece: x + 3 = 77.78 + 3 = 80.78 meters (approximately)
Third piece: (4/5)x = (4/5) * 77.78 ≈ 62.22 meters (approximately)
Therefore, the lengths of the three wire pieces are approximately:
First piece: 77.78 meters
Second piece: 80.78 meters
Third piece: 62.22 meters