document.write( "Question 3395: one board is three feet shorter than twice the length of the other board. if the two boards together are 15 ft long, how long is each board? \n" ); document.write( "

Algebra.Com's Answer #1477 by drglass(89) $\"\"$ $\"About$

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Start by naming the boards, we can call the first board x and the second board y. The problem tells us that x is three feet shorter than twice the length of y. Well, twice the length of y is $\"2y\"$ and three feet less than 2y is $\"2y+-+3\"$ , therefore \"x is three feet shorted than twice the length of y\" can be written $\"x+=+2y+-+3\"$ . The other part of the problem tells us that together the boards are 15 ft, which means $\"x+%2B+y+=+15\"$

\n" ); document.write( "So what do we have:

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$\"x+=+2y+-+3\"$ and

$\"x+%2B+y+=+15\"$

\n" ); document.write( "Now, let's subtract y from both sides of the second equation. This gives us:

\n" ); document.write( " $\"x+=+15+-+y\"$

\n" ); document.write( "Substitute this equation for x into x in the first equation

\n" ); document.write( " $\"15+-+y+=+2y+-+3\"$ .
\n" ); document.write( "add y to both sides to get $\"15+=+3y+-+3\"$ ,
\n" ); document.write( "add 3 to both sides to get $\"18+=+3y\"$ ,
\n" ); document.write( "now divide both sides by 3 to get $\"y+=+6\"$ .
\n" ); document.write( "Substitue y = 6 into the first equation and we get:

\n" ); document.write( " $\"x+=+2%2A6+-+3+=+12+-+3+=+9\"$ .
\n" ); document.write( "So one board is 6 ft and the other is 9 ft. \n" ); document.write( "

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