document.write( "Question 1201507: The ratio of Karen's beads to Sarah's beads is 7:5 . When Sarah gives 48 beads to Karen, she has 1/3 of the number of beads Karen has. During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah. How many beads did Karen lose? \n" ); document.write( "

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document.write( "The ratio of Karen's beads to Sarah's beads is 7:5 . When Sarah gives 48 beads to Karen, she has 1/3 of the number of beads Karen has. During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah. How many beads did Karen lose?  \r\n" );
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document.write( "Let the multiplicative factor be x\r\n" );
document.write( "Then originally, Karen and Sarah had 7x and 5x beads, respectively\r\n" );
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document.write( "Sarah gave 48 beads to Karen, leaving Sarah with 5x  -  48 beads, while Karen had 7x + 48, then.\r\n" );
document.write( "As Sarah’s amount at that point was  of Karen’s, we get: \r\n" );
document.write( "                                                       15x - 3(48) = 7x + 48 ---- Multiplying by LCD, 3\r\n" );
document.write( "                                                          15x - 7x = 1(48) + 3(48)\r\n" );
document.write( "                                                                8x = 4(48)\r\n" );
document.write( "                                       Multiplicative factor or \r\n" );
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document.write( "Initial amount Karen and Sarah had: 7(24) = 168, and 5(24) = 120, respectively\r\n" );
document.write( "After Sarah gives 48 beads to Karen, Sarah had 120  -  48 = 72 remaining, while Karen had 168 + 48 = 216 beads\r\n" );
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document.write( "                                      Let number Karen lost to Sarah be A\r\n" );
document.write( "                                      Then we get:\r\n" );
document.write( "                                             1,080  -  5A = 72 + A ----- Multiplying by LCD, 5  \r\n" );
document.write( "                                              -  5A  -  A = 72  -  1,080\r\n" );
document.write( "                                                     - 6A = - 1,008\r\n" );
document.write( "  Number of beads lost to Sarah, or

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