document.write( "Question 857637: A 48-foot rope is cut into three lengths. The second length of rope is twice the first length. The third length of rope is one-fifth the first length. What is the third length? \n" ); document.write( "

Algebra.Com's Answer #516678 by josmiceli(19441) $\"\"$ $\"About$

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Let the lengths = $\"+a+\"$ , $\"+b+\"$ , and $\"+c+\"$
\n" ); document.write( "-------------
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+48+\"$
\n" ); document.write( "(2) $\"+b+=+2a+\"$
\n" ); document.write( "(3) $\"+c+=+%281%2F5%29%2Aa+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Substitute (2) and (3) into (1)
\n" ); document.write( "(1) $\"+a+%2B+2a+%2B+%281%2F5%29%2Aa+=+48+\"$
\n" ); document.write( "(1) $\"+3a+%2B+%281%2F5%29%2Aa+=+48+\"$
\n" ); document.write( "Multiply both sides by $\"+5+\"$
\n" ); document.write( "(1) $\"+15a+%2B+a+=+240+\"$
\n" ); document.write( "(1) $\"+16a+=+240+\"$
\n" ); document.write( "(1) $\"+a+=+15+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+b+=+2a+\"$
\n" ); document.write( "(2) $\"+b+=+30+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+c+=+%281%2F5%29%2A15+\"$
\n" ); document.write( "(3) $\"+c+=+3+\"$
\n" ); document.write( "the 3rd length is 3 ft
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+48+\"$
\n" ); document.write( "(1) $\"+15+%2B+30+%2B+3+=+48+\"$
\n" ); document.write( "(1) $\"+48+=+48+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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