Yesterday it took 5 cleaners 4 and 1/2 hours to clean all the rooms in a hotel. there are only 3 cleaners to clean all the rooms in the hotel today. each cleaner is paid £8.20 for each hour or part of an hour they work. how much will each cleaner be paid today?

We know that
5 cleaners clean all the rooms in a hotel in 4 and 1/2 hours 
100% > 4.5 hours
x%> 1 hour
x=22.22%
divide by 4 cleaners
22.22%/4>5.56%
that means each cleaner clean a 5.56% in 1 hour

then  
3 cleaners> 3*5.56%> 16.67%  in 1 hour

16.67%> 1 hour
100%> x
x=100/16.67---> x=6 hours

find the payment of each cleaner
6*£8.20 > £49.20

the answer is
 £49.20

The household makes $424.45