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Posted by Knightmare on June 11, 2010 – 8:26 am

A group of people rented a golf course for the weekend where,at the end of each day,they would have to pay \$4 for every golf ball that was lost.On the first day,they played awful and everyone had to chip in \$30 each to cover the “lost golf balls” bill.On the second day,they played even worse and successfully managed to loss twice as many golf balls.The bill came to \$80 each,at which point Karl said “You know,we wouldn’t have to pay that much if our group wasn’t short of those five guys who quit after day one.”

On average,how many balls were lost per person per day?

This post is under “Tom” and has 14 respond so far.

### 14 Responds so far- Add one»

1. 1. John24 Said：

X = Golfers day 1
Y = # of balls lost day 1

Day 1
Y * \$4 = X * \$30
4Y = 30X

Day 2
2Y * \$4 = (X – 5) * \$80
8Y = 80X – 400

Substitute 2 * 30X for 8Y
60X = 80X – 400
400 = 20X
20 = X

20 Golfers day 1 paid \$30 per person or \$600 at \$4 per ball = 150 balls. Day 2 they lost twice as many, 300. 300 * \$4 = \$1200 / \$80 = 15 people or 5 less than day 1.

Day 1 each Golfer lost on average 7.5 balls.
Day 2 each Golfer lost on average 20 balls.

2. 2. Trcek Grega Said：

6

3. 3. Karys Said：

I agree with John. I’d say “per person per day” means we want a mean of the numbers you found. (which would be “per person each day”)

On day one, 20 person lost 150 balls.
On day two 15 person lost 300 balls.

450 balls were lost by 20 ppl in 2 days.

Mean : (150+300)balls/20ppl/2days = 11.25

That means that if everyone stayed for 2 days and lost 11 balls each approximately, they would have lost a total of 450 balls.

11.25 balls were lost per person per day.

4. 4. Chris Said：

I get the same as John24 (post 1).

5. 5. Knightmare Said：

yeah…first post got it right

Karys,how does 13.75 sound?

6. 6. Chris Said：

I can’t think of a satisfactory definition for the average number of balls lost per person per day, but your 13.75 seems the most obvious one.

7. 7. Karys Said：

Uh, looks like you did the average on day 1 + average on day 2, divided by 2.

To me it seems that the averages on day 1 and 2 cannot be “averaged” that way, since they do not take the same number of ppl into account.

First day there were 20 ppl, second day there were 15 ppl… how could I express it…?

Suppose we had one thousand ppl playing golf the first day, 1000.
Each one loses 1 ball. On day one, there are 1000 balls lost, 1 per person.

On day 2, 999 ppl quit. The 1 person left plays, and loses 2 balls.
That’s 2 balls per person.

Then if you make the average as you did, that would mean 1.5 balls per person per day were lost… while you could neglect the loss on day 2 (2 balls) against the loss on day 1 (1000), which would give 1 ball /pers./day.

8. 8. James Said：

i calculated 2.5

9. 9. Xander9009 Said：

Ok. At first I got 13.75 because it is the most obvious. However, the point made by Karys is right. So, what about ~12.86
I got that from thinking about Karys’ point.

(Btw, if 2,999 people quit out of 1,000 then there are -1,999 people playing. but the point is made nonetheless)

Although the 2 balls by the 1 person of the second day seems negligible, the numbers could change so it isn’t.

Let’s say there were half as many people, 500, and they half of them lost 1 ball, 250.

That’s 1250 balls by 1500 people. Just add the people per day and then add the balls lost per day and use those numbers.

So I added 300 and 150 = 450. And I added 20 and 15 to 35.
450 balls, 35 people. ~12.86 balls per person per day..

10. 10. Karys Said：

uh “if 2,999 people quit out of 1,000 then there are -1,999 people playing”

It is written “on day 2, … 999 ppl….

11. 11. Karys Said：

@Xander
That was what I thought at first, but you cannot say “per day” when you didn’t divide by the number of days (something I learnt from physics class…units cannot change with no reason). That way you get 12.86 balls per person. Period.
John’s calculus is good, since he separated the days, but that’s not what I think was asked (but we are on ToM, so as long as it’s interesting…).

Here, Xander, you say there are 35 ppl in all, whereas it was specified “5 players quit”, that means the 15 left are the same as 15 of the people on day 1.

On the other hand, if you said after 1st day all 20 people were fed up and quitted, and 15 OTHER people came playing on day 2, then you have a total of 35 people having lost 450 balls.

But we know that there are not 35 people, since there are 20…

You say 12.86 balls per person. What if on days 1 AND 2, all 20 ppl remained ? In that expression of things, you get :
[total of balls lost]/[people]. With the method you used, in our case, all 20 people will be counted twice, yet the numbers of days don’t infere in our problem.

Another example :

(1) 20 people on day 1, all lose the 450 balls on day 1.
Then, on day 2, everyone left. That makes 450/20 balls per person.

(2) 20 people on day 1, all lose 150 balls, day 1.
Day 2, all 20 people stay and lose 300.

In both cases, 20 people lost 450 balls in 2 days, yet the average is not the same, since on case (2) you count each people on each day separately.

12. 12. Gary Holmes Said：

1) John 24 & James:
Have u been drinking?
How to lose 7.5 balls or 2.5?
Someone split a ball into halves, and lost half ea day?

R u age 24?
Or height 24 inches?
or weight 24 tons?

2) Karys, Nightmare, Chris:
R u ok?
Temperature less than 104 F?
How to lose .25 or .75 balls?

When u split a ball into 4 quarters, make sure u would cut them equally…?

3) Xander 9009:
12.86 sounds good in the year of 9009.
But, not in 2009.

4) Karys:
Do u have to work, pls?
Sounds like: U’ve all sorts of time to do so many calcs.

5) Karl S:
U must b laughing hard by now?
U’ve got everybody running around madly, trying to lose half, quarter, or 0.86 balls every day…

Gary Holmes

13. 13. Karl Sharman Said：

I seem to be taking the blame for Knightmares’ excellent conundrum here. I have broad shoulders.
I have played golf, badly, in my time. One day I lost 7 balls and the following day I lost 6. In my humble estimation, I lost an average of 6.5 balls each day. I looked back upon my poor golfing and realised I could not have lost 6.5 balls each day as I only ever used whole balls. The mystery of averages eh? Gets me every time.

Karl

14. 14. Chris Said：

Hi GAry. The averages doesn’t have to be a whole number of balls. Another e.g. is that the average value that you throw on a die is 3.5.

Hi Karl. The problem of finding the average only exists because the number of golfer’s had changed.

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