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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<pre>
Let' start from this point

    "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."


We want to write this statement as a long proportion of three terms.


For it, write partial proportions E:C = 4:7 and C:L = 3:5 as long three terms proportion

    E:C:L = 12:21:35.


The logic for it is that 4:7 is the same as 12:21  (after multiplication by 3),
while proportion 21:35 is the same as 3:5  (after dividing by 7). 


So, we can assume that Emir gave away 12x stamps, Cillian gave away 21x stamps and Lasha gave away 35x stamps.


Next, let E be the number of stamps Emir kept.

Then the number of stamps Cillian kept was {{{(3/2)E}}},

and the number of stamps Lasha kept was {{{(4/3)*(3/2)E}}} = 2E.


We are given that the combined total number of stamps left in their collection was 738.


So, we write this equation

    E + {{{(3/2)E}}} + 2E = 738.

Hence

    2E + 3E + 4E = 738*2,  9E = 1476,  E = 1476/9 = 164.


Now, the problem says "The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself."

It means that

    12x = 164 - 20.


From it, we find

    12x = 144,  x = 144/12 = 12.


Very good.


Now we are in position to find the number of stamps Lasha gave away.  It is  35x = 35*12 = 420.


<U>ANSWER</U>.  Lasha gave away 420 stamps.
</pre>

Solved completely.