Aggregation. I want to count record in mongo and I then want to multiply that count by a field in a different collection

Question

This is Invoice Collection:

db.Invoice.insert({"InvoiceNo" : "1", "Total" : "22.50", "FoodId" : "1", "SupplierType" : "Meat"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "2", "Total" : "22.50", "FoodId" : "2", "SupplierType" : "Meat"})
WriteResult({ "nInserted" : 1 })
db.Invoice.insert({"InvoiceNo" : "3", "Total" : "12.50", "FoodId" : "3", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "3", "Total" : "12.50", "FoodId" : "3", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "4", "Total" : "12.50", "FoodId" : "4", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "5", "Total" : "15.00", "FoodId" : "5", "SupplierType" : "Meat"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "6", "Total" : "19.00", "FoodId" : "6", "SupplierType" : "Meat"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "7", "Total" : "10.00", "FoodId" : "7", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "8", "Total" : "10.00", "FoodId" : "8", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })    
db.Invoice.insert({"InvoiceNo" : "9", "Total" : "10.00", "FoodId" : "9", "SupplierType" : "Veg"})
WriteResult({ "nInserted" : 1 })   
db.Invoice.insert({"InvoiceNo" : "10", "Total" : "25.00", "FoodId" : "10", "SupplierType" : "Meat"})
WriteResult({ "nInserted" : 1 })

And this is Food Collection:

db.Food.insert({"FoodId" : "1", "FoodType" : "Steak","BestBeforeDate" : "07/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "2", "FoodType" : "Steak","BestBeforeDate" : "07/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "3", "FoodType" : "Carrot","BestBeforeDate" : "09/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "3", "FoodType" : "Carrot","BestBeforeDate" : "17/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "4", "FoodType" : "Peas","BestBeforeDate" : "09/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "5", "FoodType" : "Ribbs","BestBeforeDate" : "05/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "6", "FoodType" : "Ribbs","BestBeforeDate" : "05/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "7", "FoodType" : "Chips","BestBeforeDate" : "30/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "8", "FoodType" : "Chips","BestBeforeDate" : "30/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "9", "FoodType" : "Chips","BestBeforeDate" : "30/05/2018",})
WriteResult({ "nInserted" : 1 })    
db.Food.insert({"FoodId" : "10", "FoodType" : "Chicken","BestBeforeDate" : "30/05/2018",})
WriteResult({ "nInserted" : 1 })

I want to multiply the total by the count function for the Food Collection. Next I want to count how many records where FoodType is equal to "Steak". I want to multiply the result from the count by the total in the Invoice Collection.

This is the command that I thought would work:

db.Food.aggregate(
  [
    { $project: 
      { date: 1, item: 1, 
        total: { $multiply: 
          [
            {"FoodType": "Carrot"}.count(), "Total"}
          ]
        }
      }
    }
  ]
) 

I want to count the number of steak entries in the Food Table. Then I want to multiply that result by the total corresponding price in the Invoice Table.