Question 1210616
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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?
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Emir:    E
Cillian: C
Lasha:  L
Ratio of E:C = 4:7
Ratio of C:L = 3:5
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 
to 3(7):5(7) = 21:35
We now have the ratio of the 3 donors as: E:C:L = 12:21:35
As such, E(Emir), C(Cillian), and L(Lasha) gave away 12x, 21x, and 35x stamps, respectively, with x being the MULTIPLICATIVE FACTOR

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
And, as Cillian kept {{{3/2}}} as many stamps as Emir did, the number Cillian kept was {{{(3/2)(12x + 20)}}} = 18x + 30 
Now, since Lasha kept {{{4/3}}} as many as Cillian, Lasha kept {{{(4/3)(18x + 30)}}} = 24x + 40 stamps

As they had a combined 738 stamps left in their collections, we get the following TOTAL remaining-stamps equation: 
                 12x + 20 + 18x + 30 + 24x + 40 = 738
                                                          54x + 90 = 738
                                                                   54x = 648
                        MULTIPLICATIVE factor, or x = {{{648/54}}} = 12
        <font color = red>Lasha gave away 35x stamps (see above)</font>, or 35(12) = <font color = red>420 stamps</font></font></font></font></b></pre>