Posted by **Im** on Friday, May 18, 2012 at 12:42am.

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?

- math -
**Steve**, Friday, May 18, 2012 at 10:38am
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

## Answer this Question

## Related Questions

- Math (Please Help) - A man went to a post office to buy stamps. He bought x, 50 ...
- math - a manager bought some stamps. she gave 1/3 of them to a cashier and 1/5 ...
- Math - John bought some stamps. He used 3/5 of then to mail letters. He had 12 ...
- aig math - David has 120 stamps. He gave 36 stamps to Maria and some to Alice. ...
- math (please help) - Timothy had a total of 238 blue and red marbles. He gave 3/...
- math - in an album, the ratio of the number of local stamps to the number of ...
- Math - Simon and Jimmy had 167 stamps altogether. Simon gave 4/7 of his stamps ...
- math - suppose you bought some 32 cent stamps and some 20 cent stamps. you spent...
- mathematics - Timothy had a total of 238 blue and red marbles. He gave 3/7 of ...
- MATH - Allen started out with x marbles. He doubled his number of marbles by ...