Accounting for Overheads- Reciprocal reapportionment

Good afternoon John and other forum members,

I am stuck and very confused with the following question and would be grateful for your help please.

The question is as follows:

A company has 3 production departments, Alpha, Beta and Gamma and 2 service departments these are Maintenance (M) and Payroll (P).

The following table shows how costs are allocated and the usage of each service dept by other service depts.

Dept Alpha Beta Gamma M P
Costs $3,000 $4,000 $2,000 $2,500 $2,700
Proportion M (%) 20 30 25 – 25
Proportion P (%) 25 25 30 20 –

My apologies if the table above does not come out correctly. I am unable to scan and attach images to the forum responses. Hopefully it will be clear.

The question requires students to:
Complete an overhead analysis sheet and re-apportion service dept overheads to production dept using the reciprocal method.

I have come close to the end of the table and currently have to re-apportion P which as it currently stands has $166 in P.

My reciprocal re-apportionment methods are as follows:
Alpha: 0.25 x $166 = $42
Beta: 0.25 x $166 = $42
Gamma 0.3 x $166 = $50
M: 0.2 x $166 = $33

However, the answer provided is:
Alpha: $41
Beta: $42
Gamma: $50
M: $33

Towards the end of the table when I have to re-apportion P for the final time, I face a similar situation. P stands at $8 towards the end of the table.

My reciprocal re-apportionment methods are as follows:
Alpha: 0.25 x $8 = $2
Beta: 0.25 x $8 = $2
Gamma 0.3 x $8 = $2
M: 0.2 x $8 = $2

However the answer provided is:

Alpha: $3
Beta: $2
Gamma: $3
M: $0

I’m confused. The differences between my answers and those provided are small. However, they still concern me. I don’t know what I have done wrong. I thought it may be due to rounding differences, and have used a few different calculators.

I still can’t understand the discrepancy and would be grateful for your assistance.