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Among the stamps that Eliot collected, 4/5 of them were local stamps and the rest were foreign stamps. After exchanging 20 local stamps for 20 foreign stamps, the number of local stamps that Eliot has becomes 8/15 of his total collection. How many local stamps did Eliot have at first?

 
 Aug 1, 2022
 #1
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Let \(l \) = local stamps and let \(f\) = foreign stamps. 

 

We have the system: 

 

\(l = {4 \over 5}(l + f)\)

\(l - 20 = {8 \over 15} (f + l) \)

 

Now, just solve for l and f...

 
 Aug 1, 2022
 #2
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l + f = 5/4l

l - 20 = 8/15 * 5/4l

l - 20 = 2/3l

3 (l - 20) = 2l

3l - 60 = 21

3l - 21 = 60

l = 60

l + f = 5/4l

f = 5/4l - l

f = (5l - 4l)/4

f = l/4, f = 60/4, f = 15

l = 60 and f = 15

 
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