Question 1105453
x is the number of items bought.
y is the price per item.


x * y = 36


if she bought 6 more items, she would have paid 3 dollars less per item and the total cost would still have been 36 dollars.


(x+6) * (y-3) = 36


from the first equation, solve for y to get y = 36/x.


in the second equation, replace y with 36/x to get (x + 6) * (36/x - 3) = 36


multiply both sides of the equation by x to get x * (x + 6) * (36/x - 3) = 36 * x


simplify to get (x^2 + 6x) * (36/x - 3) = 36x.


distribute the multiplication to get 36x - 3x^2 + 216 - 18x = 36x.


the 36x on both sides of the equation cancels out and you are left with -3x^2 + 216 - 18x = 0


reorder the terms in descending order of degree to get -3x^2 - 18x + 216 = 0


factor this equation to get x = 6 or x = -12.


x can't be negative, so x = 6.


i the equation of xy = 36, replace x with 6 to get 6y = 36.


solve for y to get y = 6.


x is the number of items bought.
y is the price per item.


she bought 6 items at 6 dollars each for a total of 36 dollars.


if she bought 6 more items, then the price per item would have been 3 dollars less.


(x+6) * (y-3) = 36


x = 6 and y = 6, therefore (6+6) * (6-3) = 36 which becomes 12 * 3 = 36 which is true.


everything checks out so your solution is that she bought 6 items.