document.write( "Question 1169905: A carpenter purchased 70 ft of redwood and 80 ft of pine for a total cost of $335. A second purchase, at the same prices, included 100 ft of redwood and 50 ft of pine for a total cost of $395. Find the cost per foot of redwood and of pine. \n" ); document.write( "

Algebra.Com's Answer #794820 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The given information gives us two equations:

\n" ); document.write( " $\"70x%2B80y+=+335\"$
\n" ); document.write( " $\"100x%2B50y+=+395\"$

\n" ); document.write( "My definite preference for solving a system of equations in this form is elimination. Multiply one or both equations by constants so that the coefficients of one of the variables are the same in the two equations; then subtract one equation from the other to eliminate that variable.

\n" ); document.write( " $\"350x%2B400y+=+1675\"$
\n" ); document.write( " $\"800x%2B400y+=+3160\"$
\n" ); document.write( " $\"450x+=+1485\"$
\n" ); document.write( " $\"x+=+1485%2F450+=+3.3\"$

\n" ); document.write( "Then substitute x=3.3 in either original equation to solve for y.

\n" ); document.write( " $\"70%283.3%29%2B80y+=+335\"$
\n" ); document.write( " $\"231%2B80y+=+335\"$
\n" ); document.write( " $\"80y+=+104\"$
\n" ); document.write( " $\"y+=+1.3\"$

\n" ); document.write( "ANSWERS: x = $3.30 per foot for redwood; y = $1.30 per foot for pine.

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