Question 697818
Before the discount the amount she would have paid = n*p, 
where n=the number of oranges, p=the original price
After the discount, the amount paid is (n+8)(p-2) [8 more oranges, 2 dollars less]
In both cases, the amount paid is $96:
np = 96 -> p = 96/n
(n+8)(p-2) = 96 -> (n + 8)(96/n - 2) = 96
Performing the arithmetic, we get
n^2 + 8n - 384 = 0
Factor:
(n+24)(n-16) = 0
Take the positive solution, n=16
So she purchases 16+8 = 24 oranges at the new price