Question 679003
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*p = 4.32}}}


Solve for n to get {{{n = 4.32/p}}}



"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) = {{{(n+12)*(p-0.03) = 4.32}}}


Expand and simplify to get


{{{(n+12)*(p-0.03) = 4.32}}}


{{{np - 0.03n + 12p - 0.36 = 4.32}}}


{{{np - 0.03n + 12p = 4.32 + 0.36}}}


{{{np - 0.03n + 12p = 4.68}}}


Now plug in {{{n = 4.32/p}}} to get 


{{{(4.32/p)p - 0.03(4.32/p) + 12p = 4.68}}}


{{{4.32 - 0.1296/p + 12p = 4.68}}}


{{{-0.1296/p + 12p = 4.68 - 4.32}}}


{{{-0.1296/p + 12p = 0.36}}}


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


{{{p(-0.1296/p) + p*12p = p*0.36}}}


{{{-0.1296 + 12p^2 = 0.36p}}}


{{{-0.1296 + 12p^2 - 0.36p = 0}}}


{{{12p^2 - 0.36p - 0.1296 = 0}}}


The equation is now in standard form {{{ap^2+bp+c=0}}}. Use the quadratic formula to solve for p


{{{p = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{p = (-(-0.36)+-sqrt((-0.36)^2-4(12)(-0.1296)))/(2(12))}}} Plug in {{{a = 12}}}, {{{b = -0.36}}}, {{{c = -0.1296}}}  


{{{p = (0.36+-sqrt(0.1296-(-6.2208)))/(24)}}}


{{{p = (0.36+-sqrt(0.1296+6.2208))/(24)}}}


{{{p = (0.36+-sqrt(6.3504))/24}}}


{{{p = (0.36+sqrt(6.3504))/24}}} or {{{p = (0.36-sqrt(6.3504))/24}}}


{{{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 <font color="red">12 cents</font>.


Let's find n.


{{{n = 4.32/p}}}


{{{n = 4.32/0.12}}}


{{{n = 36}}}


Which means that she bought <font color="red">36 stickers</font>


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 <font color="red">12 cents</font> a sticker and she bought  <font color="red">36 stickers</font>.