A 76 foot piece of rope is cut into three pieces where one piece is three times longer than the other two equal pieces. How long is each piece? (decimals allowed)

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Let the length of one of the shorter pieces be [latex]\ell[/latex]. Then, we know that two of the pieces are that length, and the third piece is [latex]3 \ell[/latex]. Since these are all pieces of a rope, all we need to do to figure out the lengths is add all those together, solve for [latex]\ell[/latex], and then plug that back in to the desired lengths: [latex]3 \ell + \ell + \ell = 76 ft.[/latex] [latex]5 \ell = 76 ft.[/latex] [latex]\ell = 15.2 ft.[/latex] Shorter pieces: [latex]\ell = \bf 15.2 ft.[/latex] Longer piece: [latex]3 \ell = \bf 45.6 ft.[/latex]

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