accounting for overheads

Hi sir.
This is a question from ACCA specimen exams June 2014;
A factory consists of two production cost centres (P and Q) and two service cost centres (X and Y). The total allocated
and apportioned overhead for each is as follows:
P Q X Y
$95,000 $82,000 $46,000 $30,000
It has been estimated that each service cost centre does work for other cost centres in the following proportions:
P Q X Y
Percentage of service cost centre X to 50 50 – –
Percentage of service cost centre Y to 30 60 10 –
The reapportionment of service cost centre costs to other cost centres fully reflects the above proportions.
After the reapportionment of service cost centre costs has been carried out, what is the total overhead for
production cost centre P?

The answer was worked out as follows;

Direct cost $95,000
Proportion of cost centre X (46,000 + (0·10*30,000))*0·50 $24,500
Proportion of cost centre Y (30,000*0·3) $9,000
Total overhead cost for P $128,500

I can’t seem to understand how the answer was worked out