A despesa fixa continuou, ao passo que a despesa variável mudou.

Both are in the pretérito perfeito (the simple past in Portuguese):

• continuou = continued
• mudou = changed

This tense is used to describe a completed situation or event in the past. In this sentence, it presents two past facts:

• the fixed expense continued
• the variable expense changed

So it sounds like a report about what happened over a certain period.

Because despesa is a feminine singular noun in Portuguese.

That means the article and adjectives must agree with it:

• a = feminine singular the
• fixa = feminine singular form of fixo/fixa
• variável = same form here for masculine and feminine singular

So:

• o custo fixo = the fixed cost
• a despesa fixa = the fixed expense

Agreement is a very important part of Portuguese grammar.

Ao passo que is a connector meaning:

• whereas
• while
• by contrast
• while on the other hand

It introduces a contrast between two clauses.

In this sentence, it highlights the difference between the two types of expense:

• one continued
• the other changed

It is a bit more formal and structured than just using mas.

Because ao passo que introduces a new clause with a contrasting idea.

Portuguese normally uses a comma before connectors like this when they link two full clauses:

• A despesa fixa continuou, ao passo que a despesa variável mudou.

This is similar to how English often uses punctuation before whereas or while in formal writing.

It can suggest both, depending on context.

Literally, continuou means continued. But with something like an expense, it often implies that it remained in place or kept going as before.

So in context, A despesa fixa continuou can feel close to:

• The fixed expense continued
• The fixed expense remained
• The fixed expense stayed the same
  (if the broader context supports that interpretation)

It does not automatically mean unchanged, but that is often the practical idea.

The repetition makes the sentence clearer and more formal.

• a despesa fixa
• a despesa variável

This parallel structure is very common in careful written Portuguese.

You could sometimes shorten it if the context is very clear, but repeating the noun is safer and more natural in formal writing. It avoids any ambiguity and makes the contrast neat and balanced.

Yes, sometimes, but the tone changes.

• mas = but
  More general and less formal.
• enquanto = can mean while or whereas
  But it can also suggest time, so it may be less precise.
• ao passo que = clearly marks contrast in a more formal way

Compare:

• A despesa fixa continuou, mas a despesa variável mudou.
  Natural, simpler.
• A despesa fixa continuou, enquanto a despesa variável mudou.
  Possible, but may sound a bit more ambiguous.
• A despesa fixa continuou, ao passo que a despesa variável mudou.
  More formal and explicitly contrastive.

Because in Portuguese, adjectives often come after the noun.

So:

• despesa fixa = fixed expense
• despesa variável = variable expense

This is the normal order in Portuguese, especially for descriptive or technical adjectives.

Putting the adjective before the noun is sometimes possible in Portuguese, but it is less common and can sound stylistic, literary, or emphatic. In this sentence, the standard order is exactly what you would expect.

They are related, but not identical.

• despesa = expense, expenditure
  Common in accounting, business, and formal contexts
• gasto = spending, expense
  Often more general or everyday
• custo = cost
  Refers more to the cost of something rather than an expense entry

In this sentence, despesa fits well because despesa fixa and despesa variável are common accounting/business expressions.

Yes, variável is an adjective here, describing despesa.

Singular:

• variável

Plural:

• variáveis

Examples:

• despesa variável = variable expense
• despesas variáveis = variable expenses

Notice the accent stays:

• variável
• variáveis

In a normal full sentence like this, yes, it is the natural choice.

• A despesa fixa continuou...
• A despesa variável mudou.

Using the article makes the sentence sound complete and standard. Without it, the phrase can sound more like a heading, label, or note:

• Despesa fixa continuou...
  possible in headlines or shorthand, but less natural in ordinary prose

So for standard written Portuguese, keeping a is best.

A rough pronunciation guide for English speakers is:

ah dehs-PEH-zah FEEK-sah kon-chee-noh-OW, ow PAH-soh keh ah dehs-PEH-zah vah-ree-AH-vel moo-DOH

A few helpful notes:

• despesa: stress on pe
• fixa: the x sounds like sh in Brazilian Portuguese here
• continuou: the ending -ou sounds roughly like ohw
• variável: stress on á
• mudou: stress on the last syllable

Pronunciation varies somewhat by region, but this gives a useful Brazil-oriented approximation.