document.write( "Question 631627: Water and grape juice concentrate were mixed in a ratio of 5 to 3 to make grape juice. After 14 cups of grape concentrate was added, the amount of water and grape concentrate was equal. How much grape juice was originally in the mixture? \n" ); document.write( "

Algebra.Com's Answer #397713 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+g+\"$ = cups of grape juice in original mixture
\n" ); document.write( "Let $\"+w+\"$ = cups of water in original mixture
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+w%2Fg+=+5%2F3+\"$
\n" ); document.write( "(2) $\"+g+%2B+14+=+w+\"$
\n" ); document.write( "---------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+%28+g+%2B+14+%29+%2F+g+=+5%2F3+\"$
\n" ); document.write( "(1) $\"+g+%2B+14+=+%285%2F3%29%2Ag+\"$
\n" ); document.write( "(1) $\"+3g+%2B+42+=+5g+\"$
\n" ); document.write( "(1) $\"+2g+=+42+\"$
\n" ); document.write( "(1) $\"+g+=+21+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+g+%2B+14+=+w+\"$
\n" ); document.write( "(2) $\"+w+=+21+%2B+14+\"$
\n" ); document.write( "(2) $\"+w+=+35+\"$
\n" ); document.write( "-------------
\n" ); document.write( "21 cups of grape juice was in the original mixture
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+w%2Fg+=+5%2F3+\"$
\n" ); document.write( "(1) $\"+35+%2F+21+=+5%2F3+\"$
\n" ); document.write( "(1) $\"+5%2F3+=+5%2F3+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );