SOLUTION: I've already tried to solve this exam question (just by trial and error) and i got the answer is Susan pay $0.09 for each sticker and she buy 48 stickers. But my teacher said th

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I've already tried to solve this exam question (just by trial and error) and i got the answer is Susan pay $0.09 for each sticker and she buy 48 stickers. But my teacher said th      Log On


   

Question 679003: I've already tried to solve this exam question (just by trial and error) and i got the answer is Susan pay $0.09 for each sticker and she buy 48 stickers.
But my teacher said the answer is Susan pay $0.36 for each sticker and she buy 13 stickers.
The problem is she didn't tell me the process to get it and because i just use trial and error, i also don't know the process to get my answer so i don't know whether it's correct or not.
Could you help me to solve this question with the step by step process ?
Here's the question.
Susan paid $4.32 for a number of stickers. If the price of a sticker was cheaper by 3 cents, she could get 12 more stickers for the same amount of money. How much did she pay for each sticker and how many stickers did she buy ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of stickers bought (before the price becomes cheaper by 3 cents) and p = price per sticker (in dollars)


"Susan paid $4.32 for a number of stickers" means that

n%2Ap+=+4.32

Solve for n to get n+=+4.32%2Fp


"If the price of a sticker was cheaper by 3 cents" tell us that if the price was really p - 0.03 dollars "she could get 12 more stickers for the same amount of money" means she can get n+12 stickers (instead of just n stickers)

This means that

(Number of Stickers)*(Price) = %28n%2B12%29%2A%28p-0.03%29+=+4.32

Expand and simplify to get

%28n%2B12%29%2A%28p-0.03%29+=+4.32

np+-+0.03n+%2B+12p+-+0.36+=+4.32

np+-+0.03n+%2B+12p+=+4.32+%2B+0.36

np+-+0.03n+%2B+12p+=+4.68

Now plug in n+=+4.32%2Fp to get

%284.32%2Fp%29p+-+0.03%284.32%2Fp%29+%2B+12p+=+4.68

4.32+-+0.1296%2Fp+%2B+12p+=+4.68

-0.1296%2Fp+%2B+12p+=+4.68+-+4.32

-0.1296%2Fp+%2B+12p+=+0.36

Then multiply everything by the LCD p to clear out the fractions

p%28-0.1296%2Fp%29+%2B+p%2A12p+=+p%2A0.36

-0.1296+%2B+12p%5E2+=+0.36p

-0.1296+%2B+12p%5E2+-+0.36p+=+0

12p%5E2+-+0.36p+-+0.1296+=+0

The equation is now in standard form ap%5E2%2Bbp%2Bc=0. Use the quadratic formula to solve for p

p+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

p+=+%28-%28-0.36%29%2B-sqrt%28%28-0.36%29%5E2-4%2812%29%28-0.1296%29%29%29%2F%282%2812%29%29 Plug in a+=+12, b+=+-0.36, c+=+-0.1296

p+=+%280.36%2B-sqrt%280.1296-%28-6.2208%29%29%29%2F%2824%29

p+=+%280.36%2B-sqrt%280.1296%2B6.2208%29%29%2F%2824%29

p+=+%280.36%2B-sqrt%286.3504%29%29%2F24

p+=+%280.36%2Bsqrt%286.3504%29%29%2F24 or p+=+%280.36-sqrt%286.3504%29%29%2F24

p+=+0.12 or p+=+-0.09

Since a negative price doesn't make much sense, we toss out p+=+-0.09

So the only solution is p=0.12

So the price per sticker is 12 cents.

Let's find n.

n+=+4.32%2Fp

n+=+4.32%2F0.12

n+=+36

Which means that she bought 36 stickers

Check:

First note that buying 36 stickers at 12 cents a piece costs a total of 36*0.12 = 4.32 dollars. So that part checks out

If you lower the price 3 cents, it drops to 9 cents per sticker. We're told that you can buy 12 more stickers (or 36+12 = 48 stickers total now) and the final price won't change.

Sure enough, multiplying 0.09 by 48 will give you 0.09*48 = 4.32 and that confirms the second bit of info given.

So something doesn't fit because these two answers aren't the answers that your teacher gave you.
Either the problem is wrong (there might be a typo in the problem) or the answer your teacher gave you is wrong (s/he might be mistaken).


So again, to sum things up, the answer is that she paid 12 cents a sticker and she bought 36 stickers.