document.write( "Question 1210616: Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their collections to a museum. The ratio of the number of stamps Emir and Cillian gave away was 4:7, while the ratio of the number of stamps Cillian and Lasha gave away was 3:5. The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself. Cillian kept 3/2 as many stamps as Emir kept, and Lasha kept 4/3 as many stamps as Cillian kept. After their donations, they had a combined total of 738 stamps left in their collections. How many stamps did Lasha give away? \n" ); document.write( "

Algebra.Com's Answer #854424 by ikleyn(53846) $\"\"$ $\"About$

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\n" ); document.write( "Emir, Cillian, and Lasha are avid collectors of vintage postage stamps.
\n" ); document.write( "During a local exhibition, they decided to donate parts of their collections to a museum.
\n" ); document.write( "The ratio of the number of stamps Emir and Cillian gave away was 4:7,
\n" ); document.write( "while the ratio of the number of stamps Cillian and Lasha gave away was 3:5.
\n" ); document.write( "The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself.
\n" ); document.write( "Cillian kept 3/2 as many stamps as Emir kept,
\n" ); document.write( "and Lasha kept 4/3 as many stamps as Cillian kept.
\n" ); document.write( "After their donations, they had a combined total of 738 stamps left in their collections.
\n" ); document.write( "How many stamps did Lasha give away?
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document.write( "Let' start from this point\r\n" );
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document.write( "    \"The ratio of the number of stamps Emir and Cillian gave away was 4:7, \r\n" );
document.write( "     while the ratio of the number of stamps Cillian and Lasha gave away was 3:5.\"\r\n" );
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document.write( "We want to write this statement as a long proportion of three terms.\r\n" );
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document.write( "For it, write partial proportions E:C = 4:7 and C:L = 3:5 as long three terms proportion\r\n" );
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document.write( "    E:C:L = 12:21:35.\r\n" );
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document.write( "The logic for it is that 4:7 is the same as 12:21  (after multiplication by 3),\r\n" );
document.write( "while proportion 21:35 is the same as 3:5  (after dividing by 7). \r\n" );
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document.write( "So, we can assume that Emir gave away 12x stamps, Cillian gave away 21x stamps and Lasha gave away 35x stamps.\r\n" );
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document.write( "Next, let E be the number of stamps Emir kept.\r\n" );
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document.write( "Then the number of stamps Cillian kept was ,\r\n" );
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document.write( "and the number of stamps Lasha kept was  = 2E.\r\n" );
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document.write( "We are given that the combined total number of stamps left in their collection was 738.\r\n" );
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document.write( "So, we write this equation\r\n" );
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document.write( "    E +  + 2E = 738.\r\n" );
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document.write( "Hence\r\n" );
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document.write( "    2E + 3E + 4E = 738*2,  9E = 1476,  E = 1476/9 = 164.\r\n" );
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document.write( "Now, the problem says \"The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself.\"\r\n" );
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document.write( "It means that\r\n" );
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document.write( "    12x = 164 - 20.\r\n" );
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document.write( "From it, we find\r\n" );
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document.write( "    12x = 144,  x = 144/12 = 12.\r\n" );
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document.write( "Very good.\r\n" );
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document.write( "Now we are in position to find the number of stamps Lasha gave away.  It is  35x = 35*12 = 420.\r\n" );
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document.write( "ANSWER.  Lasha gave away 420 stamps.\r\n" );
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