Here is what I have for this problem and I was wondering if someone could tell me if this is correct and I was not sure what to do with the hospital insurance premiums (so I was wondering if anyone could shed some light on this).

1) Prepare the entry to record the gross payroll.

Salaries and wages expense 140,000
Salaries and wages payable 140,000

2) Prepare the entry to record the employer payroll taxes.

Salaries expense 78,000
FICA taxes payable 5,850
Employees income taxes payable 33,000
Cash 39,150

Payroll tax expense 6,858
FICA taxes payable 5,850
State unemployment taxes payable 720
Federal unemployment taxes payable 288

computations:

FICA - .075 x 78,000 = 5,850
State unemployment - .020 x 36,000 = 720
Federal unemployment - .008 x 36,000 = 288


Here is the data for the problem that I used...

Employees of Harding Fabricators, Inc. earned gross wages of $140,000 during a recent two-week period. Employee withholdings and payroll tax percentages are presented below:

Federal withholding... $33,000
Hospital insurance premiums... 3,050
FICA... 7.5%
State unemployment... 2.0%
Federal unemployment... 0.8%

Only $78,000 of wages are subject to FICA, and $36,000 are subject to unemployment taxes.

Payroll tax expense 6,858
FICA taxes payable 5,850
State unemployment taxes payable 720
Federal unemployment taxes payable 288


Only this portion is the employer payroll taxes.

You've included what are deductible taxes from the employees checks with the employers taxes.

It should look like this:
Dr Salaries and wages expense 140,000
Cr FICA taxes payable 5850
Cr Employees income tax payable 33,000
Cr Cash or Wages Payable 101,150

I don't know where you got the 78,000. But the taxes deducted from employees checks doesn't add to the expense. You've already recorded the salary expense of 140,000, and then you're recording an additional 78,000 of salaries expense. There is no additional salary expense. The salaries are 140,000, and then 5850 and 33,000 are deductible from it and payable to the government agencies. The leftovers of 101,150 are either paid directly in cash, or temporarily charged to a payable, depending on the method the book is using.

You've written for the first entry to record the "gross" payroll. That's an odd way of stating it. The gross payroll is 140,000, but that's not what is payable to the employees, so doesn't make sense to put that in salaries payable. The taxes still have to be deducted. If they're actually recording this as two separate entries, it's something I've never seen before. And the entry with the 78,000 definitely is not part of the employers taxes, because that's deductions from the employees.

Oh, and please put Dr and Cr in front of the lines, so we can be absolutely sure what you're doing.