SOLUTION: A 94 ft. rope is cut into three pieces. The second piece is 2 feet longer then the shortest piece. The third is 4 feet less then twice the shortest piece. How long is each piece?
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Question 261765: A 94 ft. rope is cut into three pieces. The second piece is 2 feet longer then the shortest piece. The third is 4 feet less then twice the shortest piece. How long is each piece? Answer by Stitch(470) (Show Source):
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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:
Combine like terms
Add 2 to both sides
Divide both sides by 4
Now we can find the other lengths by replacing A with 24 in equations 1 & 2
Equation 1:
Equation 2:
Check the answers:
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We can check the answers by placing them back into eqaution 3
Equation 3:
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