Den nye jakke koster mere end den gamle.

Because jakke is a common gender noun in Danish, not a neuter noun.

• en jakke = a jacket
• Common gender nouns take den
• Neuter nouns take det

So:

• den nye jakke = the new jacket
  not det nye jakke

If the noun were neuter, you would use det, for example:

• det nye hus = the new house

After den, det, or de, the adjective normally takes the -e ending in Danish.

So:

• ny = new
• nye = new, in the definite adjective form

That is why you get:

• den nye jakke
• den gamle

This is a very common pattern:

• en ny jakke = a new jacket
• den nye jakke = the new jacket

So the -e here is not plural; it is also used in the definite form.

In Danish, when a noun has an adjective before it, the definite form is usually shown with a separate article plus a special adjective form.

Compare:

• jakken = the jacket
• den nye jakke = the new jacket

You usually do not say den nye jakken in standard Danish. That would be wrong in this context.

So the pattern is:

• definite noun alone: jakken
• definite noun with adjective: den nye jakke

Because Danish can leave out the noun when it is already understood from context, just like English can say the old one.

In this sentence, jakke has already appeared, so den gamle means:

• the old one
• more literally: the old [jacket]

This is very natural in Danish. You could say the full version:

• Den nye jakke koster mere end den gamle jakke.

But it sounds more natural and less repetitive to say:

• Den nye jakke koster mere end den gamle.

Mere end means more than and is used for comparison.

So:

• mere = more
• end = than

Together:

• koster mere end = costs more than

This is the normal way to compare quantity, degree, or amount in Danish.

Examples:

• Han arbejder mere end mig. = He works more than me.
• Det er mere end nok. = It is more than enough.

In your sentence, it compares the price of the new jacket with the old one.

Both ideas are possible in Danish, but they focus slightly differently.

• koster mere = costs more
• er dyrere = is more expensive

So these are both natural:

• Den nye jakke koster mere end den gamle.
• Den nye jakke er dyrere end den gamle.

The first talks directly about cost.
The second talks about being more expensive as a quality.

English also has both options:

• costs more
• is more expensive

Yes, in some contexts den gamle can refer to the old one/person, depending on what is understood from the situation.

But in this sentence, it clearly refers back to jakke, so it means the old jacket or the old one.

This is a general feature of Danish: adjectives with den/det/de can sometimes stand alone when the noun is obvious.

Context decides what is meant.

No, this is normal Danish main-clause word order.

The basic structure is:

• Den nye jakke = subject
• koster = verb
• mere end den gamle = comparison phrase

So it follows the common Danish pattern:

subject + verb + rest

Nothing unusual is happening here.

Because Danish often does not need a separate word corresponding to English one in this kind of structure.

English says:

• the old one

Danish often just says:

• den gamle

The noun is understood from context. In this sentence, everyone knows it means the old jacket.

So Danish is more compact here than English.

The dictionary forms are:

• gammel = old
• ny = new

In the sentence, they appear as:

• nye
• gamle

That -e ending is used because they follow den in a definite noun phrase.

So:

• en ny jakke = a new jacket
• den nye jakke = the new jacket

and:

• en gammel jakke = an old jacket
• den gamle jakke = the old jacket

Yes, that is grammatically correct.

It means the same thing, but it sounds more repetitive because jakke is repeated unnecessarily.

Danish usually prefers the shorter version when the noun is already clear:

• Den nye jakke koster mere end den gamle.

So both are correct, but the shorter one is more natural in everyday use.

Then you would use de instead of den, and the adjective would still have the -e form.

For example:

• de nye jakker = the new jackets
• de gamle = the old ones

A plural version could be:

• De nye jakker koster mere end de gamle.
• The new jackets cost more than the old ones.

This helps show that:

• den = singular common gender
• de = plural definite

Yes, jakke is a common gender noun, and yes, learners usually need to memorize the gender of Danish nouns.

You learn it together with the indefinite article:

• en jakke, not et jakke

That tells you it is common gender, which then helps you form other structures:

• den jakke
• den nye jakke

Memorizing nouns with en or et is one of the most useful habits when learning Danish.