document.write( "Question 340654: You have $100 and want to buy 100 items priced at $10, $3 and .50. What is the combination of items purchased when you must buy at least 1 of each? \n" ); document.write( "

Algebra.Com's Answer #244515 by Fombitz(32388) $\"\"$ $\"About$

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Let $\"A\"$ be the number of $10 parts, $\"B\"$ $3 parts, $\"C\"$ $0.50 parts.
\n" ); document.write( "1. $\"A%2BB%2BC=100\"$
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\n" ); document.write( " $\"10A%2B3B%2B0.5C=100\"$
\n" ); document.write( "2. $\"20A%2B6B%2BC=200\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"C=100-A-B\"$
\n" ); document.write( "Substitute into eq. 2,
\n" ); document.write( " $\"20A%2B6B%2B100-A-B=200\"$
\n" ); document.write( " $\"19A%2B5B=100\"$
\n" ); document.write( "The equation can only be satisfied when $\"19A\"$ is a multiple of $\"5\"$ .
\n" ); document.write( "In becomes a multiple of $\"5\"$ when $\"highlight%28A=5%29\"$ .
\n" ); document.write( " $\"19%285%29%2B5B=100\"$
\n" ); document.write( " $\"95%2B5B=100\"$
\n" ); document.write( " $\"5B=5\"$
\n" ); document.write( " $\"highlight%28B=1%29\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"C=100-1-5\"$
\n" ); document.write( " $\"highlight%28C=94%29\"$ \n" ); document.write( "

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