A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope? How would this equation be solved?
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Let x equal the length of the second rope. The first piece of rope is twice as long as the second piece, so its length is 2x. The third piece of rope is three times as long as the second piece of rope, so it is 3x. They all add up to 120 and the lengths are 2x, x, and 3x. Now you just set up the equation.\[2x+x+3x=120\]\[6x=120\]\[x=20\]It asks for the length of the longest piece of rope which will be 3x which is 60.
The best way to solve this is to assume of the sections of the rope as an unknown variable. We will take the smallest section, which is the second piece of rope and name is 'Y' The second piece of rope is Y The first piece is twice as long and it become 2Y The third piece is thrice as long as second piece and it becomes 3Y All of these together become 120ft. -Y+2Y+3Y= 120 - 6Y = 120 - Y = 20 Longest piece of rope will be 60ft