# The Marble Game

### Johnny vs. Vinny

As brothers, these two are competitive in every aspect of life. Just check out some of my other puzzles, and you'll see my brothers in action.

Today is a classic Marble Battle! The brother's played a series of 3 games:

## The Game Series Summary

Note: Not a real game. Bored at work today, put our clip-art library to good use! :)

Round 1 Johnny and Vinny each had a certain number of playing marbles. Johnny lost a game to Vin and had to give Vin half of his marbles.

Round 2 In the second game, Vin lost and had to give three-fourths of his marbles to Johnny, who now had thirty marbles.

Round 3 Finally, the two finished their third game. Vinny won and acquired some of Johnny's marbles.

Score Board At this point, each brother had exactly the number of marbles he had started with, and Johnny had twice as many marbles as Vinny.

## How many marbles did each have in the beginning?

From the final clue, we learn that Johnny has twice as many marbles as Vinny at both the start and finish. So, J = 2V, where J equals the amount of marbles Johnny has at the start and finish, and V is the same for Vinny.
After Round 1, Johnny gave half his marbles to Vinny. So Johnny has V marbles, and Vinny has 2V marbles.
After Round 2, Vinny gives 3/4s of his marbles to Johnny, so Vinny has 0.5V, and Johnny has V + 1.5V = 2.5V marbles. We are told Johnny now has 30 marbles, so 2.5V = 30, and V = 12. And J = 24.
So, Johnny started and ended with 24 marbles, and Vinny with 12.

• No, you answered faster than me! – Culver Kwan Apr 9 at 1:52
• @CulverKwan - Sorry. I know how that feels. I've been on your end of things many times! – Lanny Strack Apr 9 at 1:56

Let $$x$$ be the number of marbles Vinny started with.
Then Johnny has $$2x$$ marbles in the beginning.
After the first round, Johnny lost $$\frac{2x}2$$ marbles and he has $$2x-x=x$$ marbles. So Vinny got $$x$$ marbles, which is $$2x$$ marbles.
After the second round, Vinny lost $$2x\cdot\frac34=\frac32x$$ marbles and he has $$2x-\frac32x=\frac12x$$ marbles left. Then Johnny has $$x+\frac32x=\frac52x$$ marbles. But the problem said that he has $$30$$ marbles. So $$\frac52x=30, x=12$$.
So Johnny has $$2(12)=24$$ marbles and Vinny has $$12$$ marbles.

• Could someone help me mark spoiler properly? I can't do it. – Culver Kwan Apr 9 at 2:05
• Put the characters > and ! before a line to spoilerize it. For multi-line responses, there are several ways to do it. One way is to put those tags prior to each line. By the way, here is a tip for you: you can always start an "edit" on anyone else's post (and then cancel without making changes) to view the code they used. This will give you some ideas of how to mark up text. – Lanny Strack Apr 9 at 2:11
• @LannyStrack Thanks! BTW can you edit you answer on my newest question? It is now bountied. – Culver Kwan Apr 9 at 2:18
• I saw your latest hints on your bountied question, but I have no idea what the answer might be, which is why I have not submitted another guess. – Lanny Strack Apr 9 at 2:25
• @LannyStrack Maybe I will make a change for you guys to guess easier. Just stay tuned! – Culver Kwan Apr 9 at 2:26