SOLUTION: A 139 m. rope is cut into 3 pieces. One piece is 30 m. more then half the shortest piece. The third piece is twice the sum of the length of the shortest piece and 2. What are the l
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Question 261793: A 139 m. rope is cut into 3 pieces. One piece is 30 m. more then half the shortest piece. The third piece is twice the sum of the length of the shortest piece and 2. What are the lengths of the pieces? Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website! Given:
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Total length = 139m
there are 3 pieces of rope
Setup:
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Notice that each length is given in respect to the shotest piece.
Let A = the length of the shortest piece
Let B = the length of the second piece
Let C = the length of the third piece
Equation 1:
Equation 2:
Equation 3:
Solution:
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Since we know what B and C equal in terms of A, we can substitute the values into equation 3
Equation 3:
Simplify the equation
Combine like terms
Subtract 90 from both sides
Divide both sides by 4.5 *Rounded
Now we can find the other lengths by replacing A with 10.89 in equations 1 & 2
Equation 1: *Rounded
Equation 2:
Check the answers:
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We can check the answers by placing them back into eqaution 3
Equation 3: Off by .02 due to rounding
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