K's marbles started at km, and stamps at ks
L started with lm marbles and ls stamps.
after paragraph 1,
K has km/2 marbles and ks+ls/2 stamps
L has lm+km/2 marbles and ls/2 stamps
After spending and charity,
K has km/2 marbles and ks+ls/2-5 stamps
L has lm+km/2-11 marbles and ls/2 stamps
(ks+ls/2-5)/(km/2) = 1/7
(ls/2)/(lm+km/2-11) = 1/5
Now, having four unknowns and only two equations, I must assume that K started with no marbles (ks=0), and L started with no stamps (lm=0). That leaves us with
(ls/2-5)/(km/2) = 1/7
(ls/2)/(km/2-11) = 1/5
Clear fractions and rearrange terms to get
7ls - km = 70
5ls - km = -22
so, K bought 252 marbles, L bought 46 stamps
after initial giving,
K and L each had 126 marbles and 23 stamps
Then K had 18 stamps and 126 marbles
and L had 23 stamps and 115 marbles
18/126 = 1/7
23/115 = 1/5
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