Hello, sorry for taking half an hour to respond.
a) If x represents the number of students in her class, we have :
The cost of a calculator on website C : 480 : x
The cost of a calculator on website D : 480 : (x+4)
b) We call the price of a calculator on website C as a, and the price on website D is a-6
Let's also call the amount of calculators if we buy on website C as d, and the amount of calculators if we buy on website D as d + 4
We have :
a.d = (a-6)(d+4)
Break the brackets out : ad = ad-6d + 4a - 24
=> -6d + 4a - 24 = 0
Divide both sides by 2
=> -3d + 2a - 12 = 0
=> 2a = 3d + 12
So, d is divisible by 3, and a is divisible by 2 => ad is divisible by 6.
And ad x the amount of students = 480
So, we can conclude that the amount of students is a factor of 80
Let's list out all of them : 1,2,4,5,8,10,16,20,40,80.
If there was 20 students :
The price of each calculator would be : 480 : 20 = 24
If it's 6 cheaper, it would be 24-6 = 18
And she would've gotten 480 : 18 (not divisible)
If you keep replacing like that, you'll eventually get the answer. I don't have time left, so the answer is 16 students. Hope it helps.