Help with an if statement in powershell

Hello PowerShell Experts –

I have a folder with the following files in it:

-a---        12/22/2011   9:22 AM  595280896 Backup1.BAK                        
-a---          9/8/2011   9:56 AM   52839424 Backup2.BAK                        
-a---          9/8/2011   9:56 AM   52839424 Backup2.trn                        
-a---          9/8/2011   9:56 AM   52839424 Backup2a.trn                        
-a---          9/8/2011  10:03 AM  635913216 Backup3.BAK                        
-a---         9/22/2011  10:51 AM  406340608 Backup4.BAK                        
-a---         9/29/2011  10:02 AM  123945984 Backup5.BAK                        
-a---        12/22/2011   5:59 AM  290538496 Backup6.BAK                        
-a---        12/22/2011   5:59 AM  290538496 Backup6.trn                        
-a---        12/22/2011   5:59 AM  290538496 Backup6a.trn                        
-a---        12/22/2011   9:22 AM  595280896 Backup7.BAK                        
-a---         11/4/2011   1:16 PM   75187200 Backup8.BAK  

What I want to do is identify the newest .bak file and copy it to an alternate location.  I then want to identify the oldest .bak file and delete it.  In addition to deleting the oldest .bak file, I want the script to look at the date of the oldest .bak file and identify all .trn files with the same date and delete those as well.  

Below I have provided my script code:
#################### VARIABLES ####################
#
#The following variable identifies the newest file
$NewestFile = Get-ChildItem c:\Source\*.bak | Sort-Object lastwritetime -Descending | Select-Object -First 1
#The following variable identifies the oldest file
$OldestFile = Get-ChildItem c:\Source\*.bak | Sort-Object lastwritetime | Select-Object -First 1
#The following variable identifies the purge date in a MM/DD/YYYY format.
$PurgeDate = Get-ChildItem c:\Source\*.bak | Sort-Object lastwritetime | Select-Object -First 1 `
      | Select-object @{n="lastwritedate"; e={$_.lastwritetime.toshortdatestring()}}
#The following variable lists all of the *.trn files in the source folder
$TrnFiles = Get-ChildItem c:\Source\*.trn
#
#
#
#
#################### Script Code ####################
Copy-Item $NewestFile -Destination "c:\Target"

What I think needs to happen next is I need to go through each item in the $TrnFiles variable and change the lastwritetime property to a date with the mm/dd/yyyy format.  Once that is done, I can compare the date for each item in the variable and if the item’s last write time is equal to the date in the $Purgedate variable, then the item is deleted.  To do this, I tried the following:


ForEach($trnfile in $TrnFiles) {
      Select-Object @{n="lastwritedate"; e={$_.lastwritetime.toshortdatestring()}} `
      | If ($_.lastwritedate -eq $PurgeDate) {Remove-Item}
      }

The results were the following error.

The term 'If' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again.
At :line:15 char:5
+       | If <<<<  ($_.lastwritedate -eq $PurgeDate) {Remove-Item}


Is my logic correct?  If so, what am I doing wrong with the “if” statement.  

Is there a better way of doing this?

My apologies for the remedial Powershell skills.

Nick