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)

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]