I didn't test the code before saying what I said so here is a tested version of Aussiebear's + tweak:
Sub blah()
totRow = 10
Dim sht
Dim shtAry
shtAry = Array("Peaches", "London", "Paris", "New York", "Something Else")
For Each sht In shtAry
  Sheets(sht).Activate
  Base = Range("A" & totRow).Value
  Set HighlightCells = Intersect(Rows(totRow), Range("B:B,E:E,H:H,K:K,N:N,Q:Q,T:T,W:W,Z:Z,AC:AC,AF:AF,AI:AI"))
  Set adds = Intersect(Rows(totRow), Range("AJ:AQ"))
  For Each cll In HighlightCells.Cells
    For i = adds.Count To 1 Step -1
      Set v = adds.Cells(i)
      If cll.Value >= Base + v.Value Then
        v.Offset(1).Copy
        cll.PasteSpecial Paste:=xlPasteFormats
        Exit For
      End If
    Next i
  Next cll
Next sht
Application.CutCopyMode = False
End Sub
and a version which doesn't need anything to be activated/selected:
Sub blah()
totRow = 10
Set shtAry = Sheets(Array("Peaches", "London", "Paris", "New York", "Something Else"))
For Each sht In shtAry
  With sht
    Base = .Range("A" & totRow).Value
    Set HighlightCells = Intersect(.Rows(totRow), .Range("B:B,E:E,H:H,K:K,N:N,Q:Q,T:T,W:W,Z:Z,AC:AC,AF:AF,AI:AI"))
    Set adds = Intersect(.Rows(totRow), .Range("AJ:AQ"))
    For Each cll In HighlightCells.Cells
      For i = adds.Count To 1 Step -1
        Set v = adds.Cells(i)
        If cll.Value >= Base + v.Value Then
          v.Offset(1).Copy
          cll.PasteSpecial Paste:=xlPasteFormats
          Exit For
        End If
      Next i
    Next cll
  End With
Next sht
Application.CutCopyMode = False
End Sub