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

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) (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

Solve for n to get

"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) =

Expand and simplify to get

Now plug in to get

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

The equation is now in standard form . Use the quadratic formula to solve for p

Plug in , ,

or

or

Since a negative price doesn't make much sense, we toss out

So the only solution is

So the price per sticker is 12 cents.

Let's find n.

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.

RELATED QUESTIONS
Hi there, Could you please help me with the following advanced functions question? I... (answered by vleith)

3. Ginger over the course of an average work-week wanted to see how much she spent on... (answered by edjones)

Hi Please help me find this (the answers for both X& Y should be integer), the answers... (answered by math-vortex)

A car rental company has two rental rates. Rate 1 is $81 per day plus $0.18 per mile.... (answered by scott8148)

I am working on 'notations', and understand how to work out things like '5 to the power... (answered by mananth)

Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4. The (answered by oscargut,nerdybill)

I was doing an IQ game ("challenging" level) and was faced with a problem, which I solved (answered by ankor@dixie-net.com,scott8148)

You can afford a $1300 per month mortgage payment. You've found a 30-year loan at 7%... (answered by Theo)

A person's average was 64%. One the next test he got 68%. This raised his average to 65%. (answered by KMST)