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Inventory and cash paid to suppliers

hello everyone 

lets assume that the COGS= 75, Acc payable= increased by 2, and Inventory= decreased by 6

the cash paid to suppliers = 75 - 2 - 6= 67, but i can’t  understanding why i should to subtract the  decrease in inventory from the COGS logically

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You are trying to find how much you bought from suppliers and paid by cash

COGS was 75, 6 came from existing inventory so 69 (76 -6) is what you bought extra, out of this 69 bought 2 was on credit (increase in payables) and the rest 67 paid with cash

Cash paid to suppliers = Purchases - Delta Accounts payable 

and

Purchases = COGS + Delta inventory 

Then: 

Cash paid to suppliers = COGS + Delta inventory - Delta Accounts payable = 75 - 2 - 6 = 67

Purchases= Cogs- 6=69

Note-Cogs=op +purchases-cl stock

Paid to supplier=purchases- 2=67

Note-

Payment to supplier=op+purchases-closing