Question

Eric had only red pens and Kai had only blue pens. There were thrice as many red pens as blue pens. Then Eric gave 2/5 of his red pens to Kai, while Ka gave 1/2 of his blue pens to Eric.

(a) What fraction of Kai's pens were blue after that?

(b) For them to have equal nurber of pens in the end, Eric had to give Kai 7 blue pens and 8 red pens in another round of transfer.
How many pens did Eric have in the beginning?

Answer 1

(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens

2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.

Now Eric has 3x - 6x/5 = 9x/5 red pens.

Kai gave x/2 blue pens to Eric

Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10

Now Kai has x - x/2 = x/2 blue pens.

Now Kai has total x/2 + 6x/5 = 17x/10 pens.

required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17

5/17 is the answer.

(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.

23x/10 - 15 = 17x/10 + 15

(23x - 150)/10 = (17x + 150)/10

23x - 150 = 17x + 150

6x = 300

3x = 150

Eric had 150 pens in the beginning.