Temporary staff hours incremental budgeting

Hi Sir,

in the PM mar/jun 2019, question Marjun I am not clear on the last step for temporary staff, please could you clarify?

The total staff cost for the average two months are $120,000 so we can assume this is the normal monthly cost.

Included in the staff costs for the hotel is the salary of $30,000 per annum for the hotel manager and $24,000
per annum for the head chef. These are both permanent members of staff who are paid for the full year regardless
of their working hours.
The remaining staff costs relate to temporary staff who are only paid for the hours they work. If the hotel stays
open in January, half of these staff members will continue to work their current hours because their jobs are largely
unaffected by guest occupancy rates. However, the other half of the staff will work proportionately less hours to
reflect the 50% occupancy rate in January as opposed to the 90% occupancy rate of the last two months.

Staff costs $120,000
Less: manager’s salary ($2,500)
Less: chef’s salary ($2,000) ––––––––– $115,500
50% normal hours 57,750
50% at reduced hours x 50/90 32,083

The answer says it is 32,803. I didn’t understand why we do 50/90 and not simply 50%, giving us 28,875. Thank you