document.write( "Question 1082706: An ice cream shop sells sundaes in three size: small, 89¢; MEDIUM, $1.19; and large, $1.39. On a recent day, Robert sold 52 sundaes. He sold two more than twice as many as mediums as larges. If $58.98 was the total income from selling the sundaes, how many of each size did he sell? \n" ); document.write( "

Algebra.Com's Answer #696798 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of small sizes he sold
\n" ); document.write( "Let $\"+b+\"$ = number of medium sizes he sold
\n" ); document.write( "Let $\"+c+\"$ = number of large sizes he sold
\n" ); document.write( "-------------------------------------------
\n" ); document.write( "There are 3 unknowns, so 3 equations
\n" ); document.write( "are needed to solve
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+52+\"$
\n" ); document.write( "(2) $\"+b+=+2c+%2B+2+\"$
\n" ); document.write( "(3) $\"+.89a+%2B+1.19b+%2B+1.39c+=+58.98+\"$
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "(3) $\"+89a+%2B+119b+%2B+139c+=+5898+\"$
\n" ); document.write( "plug 2 into 1
\n" ); document.write( "(1) $\"+a+%2B+%28+2c+%2B+2+%29+%2B+c+=+52+\"$
\n" ); document.write( "(1) $\"+a+=+50+-+3c+\"$
\n" ); document.write( "Plug (1) and (2) into (3)
\n" ); document.write( "(3) $\"+89%2A%28+50+-+3c+%29+%2B+119%2A%28+2c+%2B+2+%29+%2B+139c+=+5898+\"$
\n" ); document.write( "(3) $\"+4450+-+267c+%2B+238c+%2B+238+%2B+139c+=+5898+\"$
\n" ); document.write( "(3) $\"+377c+-+267c+=+5898+-+4450+-+238+\"$
\n" ); document.write( "(3) $\"+110c+=+1210+\"$
\n" ); document.write( "(3) $\"+c+=+11+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+b+=+2c+%2B+2+\"$
\n" ); document.write( "(2) $\"+b+=+2%2A11+%2B+2+\"$
\n" ); document.write( "(2) $\"+b+=+24+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+=+50+-+3c+\"$
\n" ); document.write( "(1) $\"+a+=+50+-+3%2A11+\"$
\n" ); document.write( "(1) $\"+a+=+17+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "17 = number of small sizes he sold
\n" ); document.write( "24 = number of medium sizes he sold
\n" ); document.write( "11 = number of large sizes he sold
\n" ); document.write( "--------------------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(3) $\"+.89a+%2B+1.19b+%2B+1.39c+=+58.98+\"$
\n" ); document.write( "(3) $\"+.89%2A17+%2B+1.19%2A24+%2B+1.39%2A11+=+58.98+\"$
\n" ); document.write( "(3) $\"+15.13+%2B+28.56+%2B+15.29+=+58.98+\"$
\n" ); document.write( "(3) $\"+58.98+=+58.98+\"$
\n" ); document.write( "OK
\n" ); document.write( "You can check (1) and (2)\r
\n" ); document.write( "
\n" ); document.write( "
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