document.write( "Question 130046: Keith works at coffee shop, where a 10 oz cup of coffee costs $1.05, a 14oz cup of coffee costs $1.35, and a 20 oz cup of coffee costs $1.65. During a busy day, Keith served 34 cups of coffee, emptying five 96 oz pots while collecting a total of $45. How many cups of each size did Keith fill? \n" ); document.write( "

Algebra.Com's Answer #95048 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"a\"$ = number of 10 oz cups
\n" ); document.write( " $\"b\"$ = number of 14 oz cups
\n" ); document.write( " $\"c\"$ = number of 20 oz cups
\n" ); document.write( " $\"105a+%2B+135b+%2B+165c+=+4500\"$
\n" ); document.write( " $\"21a+%2B+27b+%2B+33c+=+900\"$
\n" ); document.write( "(1) $\"7a+%2B+9b+%2B+11c+=+300\"$
\n" ); document.write( "(2) $\"a+%2B+b+%2B+c+=+34\"$
\n" ); document.write( "(3) $\"10a+%2B+14b+%2B+20c+=+5%2A96\"$
\n" ); document.write( "From (2):
\n" ); document.write( "(4) $\"c+=+34+-+a+-+b\"$
\n" ); document.write( "Substitute this in (1)
\n" ); document.write( "(1) $\"7a+%2B+9b+%2B+11c+=+300\"$
\n" ); document.write( " $\"7a+%2B+9b+%2B+11%2A%2834+-+a+-+b%29+=+300\"$
\n" ); document.write( " $\"7a+%2B+9b+%2B+374+-+11a+-+11b+=+300\"$
\n" ); document.write( " $\"-4a+-+2b+=+-+74\"$
\n" ); document.write( " $\"2a+%2B+b+=+37\"$
\n" ); document.write( "(5) $\"b+=+37+-+2a\"$
\n" ); document.write( "Substitute (4) and (5) in (3)
\n" ); document.write( "(3) $\"10a+%2B+14b+%2B+20c+=+5%2A96\"$
\n" ); document.write( " $\"10a+%2B+14%2A%2837+-+2a%29+%2B+20%2A%2834+-+a+-+b%29+=+5%2A96\"$
\n" ); document.write( " $\"10a+%2B+518+-+28a+%2B+680+-+20a+-+20b%29+=+5%2A96\"$
\n" ); document.write( " $\"-38a+-+20b+=+480+-+518+-+680\"$
\n" ); document.write( " $\"38a+%2B+20b+=+718\"$
\n" ); document.write( "substitute (5) for $\"b\"$
\n" ); document.write( " $\"38a+%2B+20%2A%2837+-+2a%29++=+718\"$
\n" ); document.write( " $\"38a+%2B+740+-+40a+=+718\"$
\n" ); document.write( " $\"-2a+=+-22\"$
\n" ); document.write( " $\"a+=+11\"$
\n" ); document.write( "(5) $\"b+=+37+-+2a\"$
\n" ); document.write( " $\"b+=+37+-+2%2A11\"$
\n" ); document.write( " $\"b+=+15\"$
\n" ); document.write( "(4) $\"c+=+34+-+a+-+b\"$
\n" ); document.write( " $\"c+=+34+-+11+-+15\"$
\n" ); document.write( " $\"c+=+8\"$
\n" ); document.write( "Keith filled $\"11\"$ 10 oz cups, $\"15\"$ 14 oz cups,
\n" ); document.write( "and $\"8\"$ 20 oz cups
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"7a+%2B+9b+%2B+11c+=+300\"$
\n" ); document.write( " $\"7%2A11+%2B+9%2A15+%2B+11%2A8+=+300\"$
\n" ); document.write( " $\"77+%2B+135+%2B+88+=+300\"$
\n" ); document.write( " $\"300+=+300\"$
\n" ); document.write( "(2) $\"a+%2B+b+%2B+c+=+34\"$
\n" ); document.write( " $\"11+%2B+15+%2B+8+=+34\"$
\n" ); document.write( " $\"34+=+34\"$
\n" ); document.write( "(3) $\"10a+%2B+14b+%2B+20c+=+5%2A96\"$
\n" ); document.write( " $\"10%2A11+%2B+14%2A15+%2B+20%2A8+=+480\"$
\n" ); document.write( " $\"110+%2B+210+%2B+160+=+480\"$
\n" ); document.write( " $\"480+=+480\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );