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The purchase price of Master Wang's math problem is 45.
This question has been asked many times, but it is actually very simple. This is my previous answer:

Integral method:

Other assets that have not been exchanged are not counted.

Before all the exchanges, Master Wang's property was a pair of shoes, 80 yuan (a pair of 40 yuan and a pair of 80 yuan), 100 yuan in real money (later used to return to neighbors). *** 100+80= 180 yuan.

After all the money has been exchanged, Master Wang's property is that there are no shoes, and 35 yuan is real money (the change is kept in 35 yuan).

Total loss 180-35= 145 yuan.

Step by step:

Step 1: The customer bought shoes and gave fake coins. At this step, Master Wang gave them shoes, got counterfeit money and lost to 80 yuan.

Step 2: find a neighbor to exchange money, give counterfeit money and get real money. In this step, you earn 100-80=20 yuan.

Step 3: Change the customer and give it to 65 yuan. At this point, the loss is 65-20=45 yuan.

Step 4: Return the money to the neighbors. At this point, the loss is 100+45= 145 yuan.

Equivalent method:

Master Wang first exchanged counterfeit money of 100 yuan with his neighbor for real money of 100 yuan, and then returned the real money of 100 yuan to his neighbor, so there was no exchange between Master Wang and his neighbor. So Master Wang's loss is 80 yuan shoes +65 yuan change = 145 yuan.

The results of the three methods are the same.