document.write( "Question 1013311: A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and pens. \n" ); document.write( "

Algebra.Com's Answer #629570 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = the cost of a box of pencils
\n" ); document.write( "Let $\"+b+\"$ = the cost of a box of pens
\n" ); document.write( "----------------------------------
\n" ); document.write( "(1) $\"+3a+%2B+2b+=+6+\"$
\n" ); document.write( "(2) $\"+2a+%2B+4b+=+8+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and subtract (2) from (1)
\n" ); document.write( "(1) $\"+6a+%2B+4b+=+12+\"$
\n" ); document.write( "(2) $\"+-2a+-+4b+=+-8+\"$
\n" ); document.write( "--------------------
\n" ); document.write( " $\"+4a+=+4+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+3a+%2B+2b+=+6+\"$
\n" ); document.write( "(1) $\"+3%2A1+%2B+2b+=+6+\"$
\n" ); document.write( "(1) $\"+3+%2B+2b+=+6+\"$
\n" ); document.write( "(1) $\"+2b+=+3+\"$
\n" ); document.write( "(1) $\"+b+=+1.5+\"$
\n" ); document.write( "---------------
\n" ); document.write( "A box of pencils costs $1
\n" ); document.write( "A box of pens costs $1.50
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+2a+%2B+4b+=+8+\"$
\n" ); document.write( "(2) $\"+a+%2B+2b+=+4+\"$
\n" ); document.write( "(2) $\"+1+%2B+2%2A1.5+=+4+\"$
\n" ); document.write( "(2) $\"+1+%2B+3+=+4+\"$
\n" ); document.write( "(2) $\"+4+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );