document.write( "Question 1039437: terry bought some gum and candy. the number of packages of gum was one more than the number of mints. the number of mints was three the number of candy bars. if gum was 24 cents a package, mints were 10 cwnts each and candy bar were 35 cents each, how many of each did he get for $5.72 \n" ); document.write( "

Algebra.Com's Answer #654272 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of packages of gum Terry bought
\n" ); document.write( "Let $\"+b+\"$ = number of mints
\n" ); document.write( "Let $\"+c+\"$ = number of candy bars
\n" ); document.write( "------------------------------
\n" ); document.write( "(1) $\"+a+=+b+%2B+1+\"$
\n" ); document.write( "(2) $\"+b+=+3c+\"$
\n" ); document.write( "(3) $\"+24a+%2B+10b+%2B+35c+=+572+\"$ ( in cents )
\n" ); document.write( "-------------------------------------
\n" ); document.write( "There are 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "(2) $\"+c+=+b%2F3+\"$
\n" ); document.write( "Substitute (2) into (3)
\n" ); document.write( "(3) $\"+24a+%2B+10b+%2B+35%2A%28+b%2F3%29+=+572+\"$
\n" ); document.write( "Substitute (1) into (3)
\n" ); document.write( "(3) $\"+24%2A%28+b+%2B+1+%29+%2B+10b+%2B+35%2A%28+b%2F3+%29+=+572+\"$
\n" ); document.write( "(3) $\"+24b+%2B+24+%2B+10b+%2B+%2835%2F3%29%2Ab+=+572+\"$
\n" ); document.write( "Multiply both sides by $\"+3+\"$
\n" ); document.write( "(3) $\"+3%2A34b+%2B+3%2A24+%2B+35b+=+3%2A572+\"$
\n" ); document.write( "(3) $\"+102b+%2B+72+%2B+35b+=+1716+\"$
\n" ); document.write( "(3) $\"+137b+=+1644+\"$
\n" ); document.write( "(3) $\"+b+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+=+b+%2B+1+\"$
\n" ); document.write( "(1) $\"+a+=+12+%2B+1+\"$
\n" ); document.write( "(1) $\"+a+=+13+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+c+=+b%2F3+\"$
\n" ); document.write( "(2) $\"+c+=+12%2F3+\"$
\n" ); document.write( "(2) $\"+c+=+4+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "He bought 13 pkgs of gum
\n" ); document.write( "He bought 12 mints
\n" ); document.write( "He bought 4 candy bars
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"+24a+%2B+10b+%2B+35c+=+572+\"$ ( in cents )
\n" ); document.write( "(3) $\"+24%2A13+%2B+10%2A12+%2B+35%2A4+=+572+\"$
\n" ); document.write( "(3) $\"+312+%2B+120+%2B+140+=+572+\"$
\n" ); document.write( "(3) $\"+572+=+572+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );