document.write( "Question 1042468: Your company reached it sales goals for the year so you decide to buy dinner for your 45 employees. You find a restaurant that gives you a good deal on chicken dinners at $9 each, salmon dinners at $12 each and steak dinners at $15 each. The number of chicken dinners you order is half the sum of salmon and steak dinners. If the total coast of all the meals is $525, how many of each type of dinner do you buy? \n" ); document.write( "

Algebra.Com's Answer #657445 by josmiceli(19441) $\"\"$ $\"About$

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You need a total of 45 dinners
\n" ); document.write( "Let $\"+a+\"$ = number of chicken dinners ordered
\n" ); document.write( "Let $\"+b+\"$ = number of salmon dinners ordered
\n" ); document.write( "Let $\"+c+\"$ = number of steak dinners ordered
\n" ); document.write( "----------------------------------------
\n" ); document.write( "(1) $\"+a+=+%281%2F2%29%2A%28+b+%2B+c+%29+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+45+\"$
\n" ); document.write( "(3) $\"+9a+%2B+12b+%2B+15c+=+525+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+2a+=+b+%2B+c+\"$
\n" ); document.write( "(1) $\"+c+=+2a+-+b+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+2a+-+b+=+45+\"$
\n" ); document.write( "(2) $\"+3a++=+45+\"$
\n" ); document.write( "(2) $\"+a+=+15+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+c+=+2a+-+b+\"$
\n" ); document.write( "(1) $\"+c+=+2%2A15+-+b+\"$
\n" ); document.write( "(1) $\"+c+=+30+-+b+\"$
\n" ); document.write( "Substitute (1) into (3)
\n" ); document.write( "(3) $\"+9a+%2B+12b+%2B+15c+=+525+\"$
\n" ); document.write( "(3) $\"+9%2A15+%2B+12b+%2B+15%2A%28+30+-+b+%29+=+525+\"$
\n" ); document.write( "(3) $\"+135+%2B+12b+%2B+450+-+15b+=+525+\"$
\n" ); document.write( "(3) $\"+-3b+=+525+-+585+\"$
\n" ); document.write( "(3) $\"+3b+=+60+\"$
\n" ); document.write( "(3) $\"+b+=+20+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(1) $\"+c+=+2a+-+b+\"$
\n" ); document.write( "(1) $\"+c+=+2%2A15+-+20+\"$
\n" ); document.write( "(1) $\"+c+=+30+-+20+\"$
\n" ); document.write( "(1) $\"+c+=+10+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "15 chicken dinners were ordered
\n" ); document.write( "20 salmon dinners were ordered
\n" ); document.write( "10 steak dinners were ordered
\n" ); document.write( "--------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+a+=+%281%2F2%29%2A%28+b+%2B+c+%29+\"$
\n" ); document.write( "(1) $\"+15+=+%281%2F2%29%2A%28+20+%2B+10+%29+\"$
\n" ); document.write( "(1) $\"+15+=+30%2F2+\"$
\n" ); document.write( "(1) $\"+15+=+15+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+45+\"$
\n" ); document.write( "(2) $\"+15+%2B+20+%2B+10+=+45+\"$
\n" ); document.write( "(2) $\"+45+=+45+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+9a+%2B+12b+%2B+15c+=+525+\"$
\n" ); document.write( "(3) $\"+9%2A15+%2B+12%2A20+%2B+15%2A10+=+525+\"$
\n" ); document.write( "(3) $\"+135+%2B+240+%2B+150+=+525+\"$
\n" ); document.write( "(3) $\"+525+=+525+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );