document.write( "Question 401803: A store had a sale on t–shirts, during which they sold 186 t–shirts in three sizes, small, medium
\n" ); document.write( "and large, and they made $1,892. Smalls sell for $8 each, mediums sell for $10 each,
\n" ); document.write( "and larges sell for $12 each. The total number of smalls and larges sold was 30 more than
\n" ); document.write( "the number of mediums sold. How many of each size t–shirt was sold? \n" ); document.write( "

Algebra.Com's Answer #284341 by josmiceli(19441) $\"\"$ $\"About$

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$\"s\"$ = number of small t-shirts
\n" ); document.write( " $\"m\"$ = number of medium t-shirts
\n" ); document.write( " $\"l\"$ = number of large t-shirts
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"s+%2B+m+%2B+l+=+186\"$
\n" ); document.write( "(2) $\"8s+%2B+10m+%2B+12l+=+1892\"$
\n" ); document.write( "(3) $\"s+%2B+l+=+m+%2B+30\"$
\n" ); document.write( "---------------------
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "From (3):
\n" ); document.write( "(3) $\"s+-+m+%2B+l+=+30\"$
\n" ); document.write( "Now add (1) and (3)
\n" ); document.write( "(1) $\"s+%2B+m+%2B+l+=+186\"$
\n" ); document.write( "(3) $\"s+-+m+%2B+l+=+30\"$
\n" ); document.write( " $\"2s+%2B+2l+=+216\"$
\n" ); document.write( " $\"s+%2B+l+=+108\"$
\n" ); document.write( "Subtract (3) from this equation:
\n" ); document.write( " $\"s+%2B+l+=+108\"$
\n" ); document.write( " $\"-s+-+l+=+-m+-+30\"$
\n" ); document.write( " $\"0+=+-m+%2B+78\"$
\n" ); document.write( " $\"m+=+78\"$
\n" ); document.write( "From above,
\n" ); document.write( " $\"s+=+108+-+l\"$
\n" ); document.write( "Plug this into (2)
\n" ); document.write( "(2) $\"8%2A%28108+-+l%29+%2B+10%2A78+%2B+12l+=+1892\"$
\n" ); document.write( " $\"864+-+8l+%2B+780+%2B+12l+=+1892\"$
\n" ); document.write( " $\"4l+=+1892+-+780+-+864\"$
\n" ); document.write( " $\"4l+=+248\"$
\n" ); document.write( " $\"l+=+62\"$
\n" ); document.write( "and, also,
\n" ); document.write( " $\"s+=+108+-+l\"$
\n" ); document.write( " $\"s+=+108+-+62\"$
\n" ); document.write( " $\"s+=+46\"$
\n" ); document.write( "46 = number of small t-shirts sold
\n" ); document.write( "78 = number of medium t-shirts sold
\n" ); document.write( "62 = number of large t-shirts sold
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"8%2A46+%2B+10%2A78+%2B+12%2A62+=+1892\"$
\n" ); document.write( " $\"368+%2B+780+%2B+744+=+1892\"$
\n" ); document.write( " $\"1892+=+1892\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"46+%2B+78+%2B+62+=+186\"$
\n" ); document.write( " $\"186+=+186\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );