document.write( "Question 1030109: John bought some vases for $1344. 5 of them were broken during delivery. He then sold the rest of the vases each at $80 more than its original cost. He made no overall gain or loss. Find the number of vases John bought. \n" ); document.write( "

Algebra.Com's Answer #645029 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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John bought some vases for $1344.
\n" ); document.write( " 5 of them were broken during delivery.
\n" ); document.write( " He then sold the rest of the vases each at $80 more than its original cost.
\n" ); document.write( " He made no overall gain or loss.
\n" ); document.write( " Find the number of vases John bought.
\n" ); document.write( ":
\n" ); document.write( "let v = no. of vases he bought
\n" ); document.write( "then, since 5 were broken;
\n" ); document.write( "(v-5) = no. of vases he sold
\n" ); document.write( ":
\n" ); document.write( " $\"1344%2Fv\"$ = his cost for each vase
\n" ); document.write( "and
\n" ); document.write( " $\"1344%2Fv\"$ + 80 = selling price of each vase
\n" ); document.write( ":
\n" ); document.write( "No overall gain, therefore
\n" ); document.write( "(v-5)*( $\"1344%2Fv\"$ +80) = 1344
\n" ); document.write( "( $\"1344%2Fv\"$ +80) = $\"1344%2F%28%28v-5%29%29\"$
\n" ); document.write( " $\"%28%281344%2B80v%29%29%2Fv\"$ = $\"1344%2F%28%28v-5%29%29\"$
\n" ); document.write( "cross multiply
\n" ); document.write( "1344v = (1344+80v)(v-5)
\n" ); document.write( "FOIL the right side
\n" ); document.write( "1344v = 1344v - 6720 + 80v^2 - 400v
\n" ); document.write( "Subtract 1344v from both sides, form a quadratic equation
\n" ); document.write( "0 = 80v^2 - 400v - 6720
\n" ); document.write( "Simplify, divide equation by 80
\n" ); document.write( "v^2 - 5v - 84 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(v-12)(v+7) = 0
\n" ); document.write( "The positive solution
\n" ); document.write( "v = 12 vases purchased originally
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if that works out
\n" ); document.write( "1344/12 = $112 each
\n" ); document.write( "7(112+80) = $1344, total return on 7 vases sold
\n" ); document.write( " \n" ); document.write( "

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