# Percent problem

1. Sep 6, 2004

### Omid

A fruit dealer bought apples at 18 cents a dozen. He sold 80% of them at the rate of 2 for 5 cents and the remainder at the rate of 5 for 2 cents, gaining 58 cents on the transaction.
How many apples did he buy ?

Can you give me some hints please ?
Thanks

2. Sep 6, 2004

### needhelpperson

ok you know that Earnings - cost = profit

just to get you started. You can set up the equation using the rate for each apple and use the number of apples as the unknown.

for instance 18 cents/12 apples = 1.5 cents per apple

so 1.5 * x = costs where x is the number of apples. i hope this will helped

3. Sep 7, 2004

### Omid

I need more help

May I ask for more help ?
Thanks alot

4. Sep 7, 2004

### needhelpperson

alright....

earnings = 4x/5 * (5/2) + x/5*(2/5)

does that help?

5. Sep 7, 2004

### HallsofIvy

Staff Emeritus
Pretty much the same as needhelpperson said, phrased differently:

Let x be the number of apples he bought. That would be x/12 dozen and paid 18 cents for each dozen: 18(x/12)= 3x/2 cents paid for the apples.
80% of them is 0.8x (that is needhelppersons "(4/5)x") If he sold that many at "2 for 5 cents" then he got 5/2 cents for each one for a total of (0.8x)(5/2)= 2.0x cents.
The "remainder" of the apples is x- 0.8x= 0.2x He sold them for "5 for 2 cents or 2/5 cents each: that would bring in (0.2x)(2/5)= 0.08x cents.

Putting all of that together: he got a total of 2.0x+ 0.08x= 2.08x cents for the apples. He paid 3x/2= 1.5x cents for the apples and so made a profit of
2.08x- 1.5x= 0.58x cents. Since we are told that he earned a profit of 58 cents, 0.58x= 58 (any time you see a formula that simple in a "book problem" you know you are the right track!) x= 58/0.58= 10. The man bought, and sold, 10 apples.
(Note on "style". It is a really, really good idea to give the answer to a "word problem" in a complete sentence. It will amaze and impress your teacher!)

6. Sep 7, 2004

### needhelpperson

Uhh, 58/.58 is NOT 10. It's 10 times more than that....

7. Sep 7, 2004

### HallsofIvy

Staff Emeritus
Well, if you want to be picky about it!

(thanks for the correction.)

8. Sep 7, 2004

### Omid

Thank you very much (needhelpperson,HallsofIvy)

9. Sep 7, 2004

### needhelpperson

hey, i admire your knowledge. But it's not often i get to correct you...

10. Sep 7, 2004

### HallsofIvy

Staff Emeritus
Don't worry, I'll keep making mistakes- just for you!