document.write( "Question 1184088: Juliet gave her 1/5 of her marbles to Ken. After that, Ken gave 2/3 of what he had and an additional 4 more marbles to Juliet. Then, Juliet lost 29 marbles on the way home. In the end, Juliet had 97 marbles and Ken had 21 marbles left. How many marbles did each of them have at first? \n" ); document.write( "

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\n" ); document.write( "Juliet gave her 1/5 of her marbles to Ken. After that, Ken gave 2/3 of what he had and an additional 4 more marbles to Juliet. Then, Juliet lost 29 marbles on the way home. In the end, Juliet had 97 marbles and Ken had 21 marbles left. How many marbles did each of them have at first?
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Let original amounts Juliet and Ken had, be J, and K, respectively\r\n" );
document.write( "After giving Ken  of her marbles, Juliet had  remaining \r\n" );
document.write( "After receiving  of Juliet's marbles, Ken then had:   \r\n" );
document.write( "After giving  of what he had and an additional 4 more marbles to Juliet, Ken then had:  remaining\r\n" );
document.write( "Since Ken had a final count of 21 marbles, we then get:   \r\n" );
document.write( "\r\n" );
document.write( "After receiving  and an additional 4 more marbles from Ken, Juliet then had:  remaining\r\n" );
document.write( "Since Juliet lost 29 marbles and ended up with 97 marbles, we then get: \r\n" );
document.write( "  J +  5K = 375 ------ eq (i)\r\n" );
document.write( "14J + 10K = 1,830 ---- eq (ii)\r\n" );
document.write( " 2J + 10K = 750 ------ Multiplying eq (i) by 2 ------- eq (iii) \r\n" );
document.write( "      12J = 1,080 ---- Subtracting eq (iii) from eq (ii)\r\n" );
document.write( "Original number of marbles Juliet had, or  \r\n" );
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document.write( "90 + 5K = 375 ------- Substituting 90 for J in eq (i)\r\n" );
document.write( "     5K = 375 - 90\r\n" );
document.write( "     5K = 285\r\n" );
document.write( "Original number of marbles Ken had, or

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