Inventory beginning of year $80,000
Inventory, end of year $55,000
Accounts payable, beginning of year $25,000
Accounts payable, end of year $15,000
Cost of goods sold $175,000
Cash payments for inventory (assume all purchases of inventory are on account) ?

First you have to calculate the amount of purchases. So start with your beginning Inventory plus COGS minus ending inventory equals purchases.

Now take your beginning accounts payable plus purchases minus ending accounts payable equals cash payments.