document.write( "Question 184241: I believe the answers are 60, 30, 10 but can't figure out the formula to get there. Thanks! The management of Bozo Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size and full-size cars. Compacts cost $12,000 each, intermediates cost $18,000 and full-size cost $24,000 each. If they purchase twice as many compacts as intermediate and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. The entire budget must be spent.\r
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Algebra.Com's Answer #138404 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"c\"$ = number of compacts bought
\n" ); document.write( "Let $\"i\"$ = number of intermediates bought
\n" ); document.write( "Let $\"f\"$ = number of full-sizes bought
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"1500000+=+12000%2Ac+%2B+18000i+%2B+24000f\"$
\n" ); document.write( "(2) $\"c+=+2i\"$
\n" ); document.write( "(3) $\"c+%2B+i+%2B+f+=+100\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "First divide both sides of (1) by $\"1000\"$
\n" ); document.write( "(1) $\"1500000+=+12000%2Ac+%2B+18000i+%2B+24000f\"$
\n" ); document.write( "(1) $\"1500+=+12c+%2B+18i+%2B+24f\"$
\n" ); document.write( "Now divide both sides by $\"3\"$
\n" ); document.write( "(1) $\"500+=+4c+%2B+6i+%2B+8f\"$
\n" ); document.write( "Multiply both sides of (3) by $\"8\"$
\n" ); document.write( "(3) $\"8c+%2B+8i+%2B+8f+=+800\"$
\n" ); document.write( "Subtract (1) from (3)
\n" ); document.write( "(3) $\"8c+%2B+8i+%2B+8f+=+800\"$
\n" ); document.write( "(1) $\"-4c+-+6i+-+8f+=+-500\"$
\n" ); document.write( "(4) $\"4c+%2B+2i+=+300\"$
\n" ); document.write( "Substitute (2) in (4)
\n" ); document.write( "(4) $\"4%2A%282i%29+%2B+2i+=+300\"$
\n" ); document.write( "(4) $\"8i+%2B+2i+=+300\"$
\n" ); document.write( "(4) $\"10i+=+300\"$
\n" ); document.write( "(4) $\"i+=+30\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"c+=+2i\"$
\n" ); document.write( "(2) $\"c+=+60\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"c+%2B+i+%2B+f+=+100\"$
\n" ); document.write( "(3) $\"60+%2B+30+%2B+f+=+100\"$
\n" ); document.write( "(3) $\"f+=+10\"$
\n" ); document.write( "They must purchase 60 compacts, 30 intermediates,
\n" ); document.write( "and 10 full size
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"500+=+4c+%2B+6i+%2B+8f\"$
\n" ); document.write( "(1) $\"500+=+4%2A60+%2B+6%2A30+%2B+8%2A10\"$
\n" ); document.write( "(1) $\"500+=+240+%2B+180+%2B+80\"$
\n" ); document.write( "(1) $\"500+=+500\"$
\n" ); document.write( "OK \n" ); document.write( "

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