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 #854425 by MathTherapy(10837) $\"\"$ $\"About$

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document.write( "Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their\r\n" );
document.write( "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\r\n" );
document.write( "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.\r\n" );
document.write( "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\r\n" );
document.write( "combined total of 738 stamps left in their collections. How many stamps did Lasha give away?\r\n" );
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document.write( "Emir:    E\r\n" );
document.write( "Cillian: C\r\n" );
document.write( "Lasha:  L\r\n" );
document.write( "Ratio of E:C = 4:7\r\n" );
document.write( "Ratio of C:L = 3:5\r\n" );
document.write( "Since C (Cillian) obviously gave away the same amount, the ratios can be changed from E:C = 4:7 to: 4(3):7(3) = 12:21, and from C:L = 3:5 \r\n" );
document.write( "to 3(7):5(7) = 21:35\r\n" );
document.write( "We now have the ratio of the 3 donors as: E:C:L = 12:21:35\r\n" );
document.write( "As such, E(Emir), C(Cillian), and L(Lasha) gave away 12x, 21x, and 35x stamps, respectively, with x being the MULTIPLICATIVE FACTOR\r\n" );
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document.write( "Since the number of stamps Emir gave away was 20 FEWER than the number of stamps he kept for himself, he kept 20 MORE than he donated, or 12x + 20\r\n" );
document.write( "And, as Cillian kept  as many stamps as Emir did, the number Cillian kept was  = 18x + 30 \r\n" );
document.write( "Now, since Lasha kept  as many as Cillian, Lasha kept  = 24x + 40 stamps\r\n" );
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document.write( "As they had a combined 738 stamps left in their collections, we get the following TOTAL remaining-stamps equation: \r\n" );
document.write( "                 12x + 20 + 18x + 30 + 24x + 40 = 738\r\n" );
document.write( "                                                          54x + 90 = 738\r\n" );
document.write( "                                                                   54x = 648\r\n" );
document.write( "                        MULTIPLICATIVE factor, or x =  = 12\r\n" );
document.write( "        Lasha gave away 35x stamps (see above), or 35(12) = 420 stamps

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