Bunuel
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?
A. $6
B. $8
C. $9
D. $10
E. $12
Let the price for each pizza be x.
Thus, \(p*x = 96\) {no. of pizza*price of each pizza = Total sum of money John had}
=>\(p = \frac{96}{x}\) -- eqn. (1)
After the discount, reduced price of each pizza = \((x-2)\)
and thus, he could buy 4 extra pizza. So, no. of pizzas becomes \((p+4)\)
thus the equation changes to : (p+4)*(x-2) = 96
=>\(p+4 = \frac{96}{(x-2)}\) -- eqn (2)
Equating eqn. 1 and 2-
\(\frac{96}{(x-2)} = \frac{96}{x} + 4\)
=>\(\frac{96}{(x-2)} - \frac{96}{x} = 4\)
Taking LCM and solving results in-
\(4x(x-2) = 192\)
=> \(4x^2 - 8x = 192\)
=> \(x^2 -2x - 48 = 0\)
=> \((x-8)(x+6) = 0\)
=> \(x = 8 or -6\).
As the price cant be a negative value, \(x= 8\)
As x was the original price for the pizzas, i.e., price before discount, price after discount = \((x-2)\) = \(6\)
Option A.