document.write( "Question 193650: Jim gave one-third of his jellybeans to Jack, ate two-thirds of the remainder, and had 12 left over. How many jellybeans did he have originally? \n" ); document.write( "

Algebra.Com's Answer #145343 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"n\"$ = the number he had originally
\n" ); document.write( "given:
\n" ); document.write( "The amount he gave to Jack = $\"%281%2F3%29%2An\"$
\n" ); document.write( "The remainder = $\"%282%2F3%29%2An\"$
\n" ); document.write( "Two-thirds of the remainder = $\"%282%2F3%29%2A%282%2F3%29%2An\"$
\n" ); document.write( "------------------
\n" ); document.write( "The amount he ate plus the left over beans has to
\n" ); document.write( "equal $\"%282%2F3%29%2An\"$ , so
\n" ); document.write( " $\"%282%2F3%29%2A%282%2F3%29%2An+%2B+12+=+%282%2F3%29%2An\"$
\n" ); document.write( "Multiply both sides by $\"9\"$
\n" ); document.write( " $\"4n+%2B+9%2A12+=+6n\"$
\n" ); document.write( " $\"4n+%2B+108+=+6n\"$
\n" ); document.write( " $\"2n+=+108\"$
\n" ); document.write( " $\"n+=+54\"$
\n" ); document.write( "He originally had 54 jelly beans
\n" ); document.write( "check answer:
\n" ); document.write( "He gave Jack $\"%281%2F3%29%2A54+=+18\"$
\n" ); document.write( "He had left $\"%282%2F3%29%2A54+=+36\"$
\n" ); document.write( "He ate $\"%282%2F3%29%2A36+=+24\"$
\n" ); document.write( "There were $\"12\"$ left over
\n" ); document.write( "Jack's + what he ate + left overs +
\n" ); document.write( " $\"18+%2B+24+%2B+12+=+54\"$
\n" ); document.write( "OK \r
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