K bought some marbles and gave half of them to L. bought some stamps and gave half of them to K.

K used 5 stamps and L gave away 11 marbles. The ratio of the number of stamps to the number of marbles K had left then became 1:7 and the ratio of the number of stamps to the number of marbles L had left became 1:5.

How many stamps did L buy?

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

Finally,

(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

ls=46
km=252

so, K bought 252 marbles, L bought 46 stamps

check:
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

To solve this problem, we need to break it down into steps and find the missing information step by step.

Let's start by setting up some variables:
Let's assume that K initially had "x" marbles and L initially had "y" stamps.

According to the given information:
1. K gave half of the marbles to L, which means L received x/2 marbles.
2. K then bought some stamps and gave half of them to L, which means L received y/2 stamps.
3. K used 5 stamps, so she had (y/2 - 5) stamps left.
4. L gave away 11 marbles, so he had (x/2 - 11) marbles left.

Next, we know that:
The ratio of the number of stamps to the number of marbles K had left is 1:7. Therefore, we can set up the following equation:
(y/2 - 5) / (x/2 - 11) = 1/7

Similarly, the ratio of the number of stamps to the number of marbles L had left is 1:5. Therefore, we can set up another equation:
(y/2) / (x/2) - 11 = 1/5

Now, let's solve these equations simultaneously to find the values of "x" and "y".

From equation 1: (y/2 - 5) / (x/2 - 11) = 1/7
Cross-multiplying, we get: 7(y/2 - 5) = x/2 - 11
Simplifying this equation: 7y - 70 = x/2 - 11

From equation 2: (y/2) / (x/2) - 11 = 1/5
Cross-multiplying, we get: 5(y/2) = (x/2 - 11)
Simplifying this equation: 5y = x/2 - 11

Now, we can solve these two equations to find the values of "x" and "y".