Nata spent $28 on 2 dvds. at this rate, how much would 5 cost? at what rate did she spend her money

we know that

Nata spent on DVDs

so

by proportion

Find the cost of DVDs

therefore

The answer Part a) is

The cost of DVDs is

Part b) Find the unit rate

we know that

Unit Rate is the ratio of two measurements in which the second term is

so

Find the cost of DVDs

therefore

the unit rate is

The answer Part b) is

Nata spent her money at the rate  

(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