This is word for word from the question.
Some children donated boxes of books for a school fundraiser,
On average there were 10 books in each box.
Tom then brought in a box of 20 books.
This raised the average to 12 books per box.
How many boxes were there before Tom arrived?
In: Mathematics
Edit: Wow, thank you for the gold, kind redditor! I appreciate it a lot – what a nice thing to do for someone. Thank you.
Here’s another way to think about it – not that the other answers are wrong, but this one doesn’t use variables and I find it always helps to see a problem solved in more than one way.
After the first children donate their boxes, we know that the average is 10 books per box. So we could move the books around and actually put 10 in each box. Now we know we have some boxes with 10 books in them, but we don’t know how many boxes there are.
Tom comes with his 20 books. Now we have the original boxes with 10 books each and Tom’s box with 20 books. The new average is 12 per box, which means we can take some books from Tom’s box and move them into the original boxes so that there are 12 in each box (including Tom’s!).
Well, to get 12 books in Tom’s box, we would need to remove 8 of them (to move to the other boxes). And to get 12 books in the original boxes, we need to add 2 books to each of them. So Tom’s extra 8 books would go perfectly into 4 original boxes, bringing everyone’s box to 12 books!
As another response mentioned – you can check the result once you’ve found it to make sure you haven’t made any mistakes.
x/y = 10; (x+20)/(y+1) = 12
x = 10y; x+20 = 12y+12;
x = 10y; x+8 = 12y;
2y = 8;
y = 4.
There are two equations, one for the amount of books (x) and boxes (y) before Tom brought his books, and one after. You have to simplify both equations and then you can subtract the terms of the first equation from the second, eliminating the x variable. From then on you can easily find y, which is what you need.
Thankyou very much
There were 4 boxes before. So the sum of 4 boxes with an average of 10 books each means 4×10=40. Athens 40+20 new books=60. 60/5=12 so the new average is 12. I’m sure there’s an easier way to work this out but I did it by trials and error
Before: 4 boxes -> (10+10+10+10)/4=10 books/box
After: 4 boxes(10books)+1 box(20 books) -> (10+10+10+10+20)/5= 60/5=12 books/box
Help this is helpfull
What we’re looking for is :
x = number of boxes
y = total number of books (before Tom brings his box)
From the problem , we know that :
A. y/x=10 (average)
and when Tom comes in:
B. (y+20)/(x+1)=12 (new average)
So let’s eliminate y from what we know in point A:
y/x=10 which means y=10x
Now going back to point B with that info we can replace y:
(y+20)/(x+1)=12 can be written as (10x+20)/(x+1)=12
If we multiply by (x+1) we can write this equation as :
10x+20=12(x+1)
Which gives us :
10x+20=12x+12
We can continue to simplify now :
10x+8=12x
And with the same logic :
8=12x-10x
This gives me :
8=2x
And :
x=4
With that I can find y and verify my calculations :
x=4 so y=10x=40
40 books in 4 boxes gives an average of 10 books per box
40+20 books in 5 boxes gives an average of 12 books per box
The average of all the boxes is just the number of books within all the boxes divided by the total number of boxes. We don’t know how many boxes there were to start with, but we know their average is 10 so we can just treat all the original boxes as having 10 books in them each.
So it is: (20+10x)/(x + 1)=12
The number of books in all the boxes is 20 plus 10 for every box we started with. This is divided by the number of boxes we started with plus one for the box of 20. That we know ends up equaling 12. I suspect you know how to figure it out from here…
20+10x=12(1+x)
20+10x=12+12x
8+10x=12x
8=2x
4=x
Now to check our work! If we had 4 boxes of 10 to start with and add another box of 20, we have 60 books divided by 5 boxes… which is 12. That is correct!
**Please read this entire message**
—
Your submission has been removed for the following reason(s):
* Straightforward or factual queries are not allowed on ELI5. ELI5 is meant for simplifying complex concepts (Rule 2).
* Recommended subreddit(s): /r/HomeworkHelp
—
If you would like this removal reviewed, please read the [detailed rules](https://www.reddit.com/r/explainlikeimfive/wiki/detailed_rules) first. **If you believe this submission was removed erroneously**, please [use this form](https://old.reddit.com/message/compose?to=%2Fr%2Fexplainlikeimfive&subject=Please%20review%20my%20thread?&message=https://www.reddit.com/r/explainlikeimfive/comments/guft73/-/%0A%0AThe%20concept%20I%20want%20explained:%0A%0ALink%20to%20your%20search%20for%20past%20posts%20on%20the%20ELI5%20subreddit:%0A%0AHow%20is%20this%20post%20unique:) and we will review your submission.
The new box of 20 books is 10 more the the previous average.
So if Tom’s box only had 10 books then the average would still be 10. The fact that the 10 extra books increased the average from 10 to 12 means that there are now 5 boxes since 10/5 = 2, the number the average increased by.
5 Boxes including Tom’s one means that there were previously 4 boxes.
[removed]
Latest Answers