1

While studying math, I found strange part; Credit card companies use negative balances to represent when the credit card company owes the customer money, and positive balances to represent the customer owes the credit card company money.

At the beginning, the noun is plural: Credit card companies.
And then the singular nouns are used: the credit card company, the customer.

Aren't they wrong?

4

I don't find any problem in 'singular/plural' matter. The first plural is talked in a general way, considering all credit card companies. Once the companies are defined that way, the author wants to describe what happens with any credit card company. [However, I'd prefer using an indefinite article for the 2nd, 3rd, 4th and 5th boldface. Maybe, others clarify this].

My way of learning is change the example and then think about it. Let's do it here.

"Aliens respond violently if they are offended by humans in any way. When a human teases an alien, it emits strange sounds that affect's human's brain and he feels dizziness. On the other hand when an alien attacks a human, he calls for the police force!"

3

This sentence has problems, but with respect to the plural/singular distinction it is acceptable.

In the head clause, Credit card companies use, the author speaks about what all these companies do: they all use negative balances, they all use positive balances.

But in the subordinate clauses, the author is speaking of when these representations are used: in individual instances, on the statements sent one by one to customers.

This is not to say that employing the plural would be formally incorrect:

... Companies use negative balances to represent when the companies owe the customers money, and positive balances to represent the customers owe the companies.

But this could be misunderstood. It might be taken to imply that the representation is determined by the aggregate balance—the total amount owed by all customers to all companies minus the total amount owed by all companies to all customers.

In this case, of course, that would be so absurd that nobody would actually understand it that way. But in other contexts, an aggregate reading might be reasonable.

In the table below I employ a yellow highlight when the customers owe the companies more than $800B and a blue highlight when the customers owe the companies less than $750B.

Consequently, we ordinarily employ this plural/singular distinction so the meaning will be unambiguous.

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