Purity will pay a third of Rose's share, which translates to 1800/3 = <<1800/3=600>>600 dollars.
Sheila has offered to pay 5 * 600 = <<5*600=3000>>3000 dollars
Combining everyone’s share of the rent will give a total of 600 + 3000 + 1800 = <<600+3000+1800=5400>>5400 dollars
#### 5400