Suppose that the relationship between price and quantity of gizmo kits we can buy is linear. When the price is $15, we can buy 6000 gizmo kits. If we lower the price we will pay to $13, we can only buy 4500 kits.

y - 15 = 1/750(x - 6000)

Step-by-step explanation:

Given that :

At price, p = $15 ; quantity, q = 6000

At price, p = $13 ; quantity, quantity = 4500

Expressing in the form (x, y) ;

(6000, 15) ; (4500, 13)

General form of a line equation :

y - y1 = m(x - x1)

x1 = 6000 ; y1 = 15 ; x2 = 4500 ; y2 = 13

The gradient, m :

(y2 - y1) / (x2 - x1)

(13 - 15) / (4500 - 6000)

- 2 / - 1500

Gradient, m = 1/750

Therefore,

y - 15 = 1/750(x - 6000)

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18