A sajt romlandó, úgyhogy a hűtőtáskába tesszük.

Yes. A is the Hungarian definite article, equivalent to the in English.

• a sajt = the cheese
• Hungarian uses a before consonant sounds and az before vowel sounds:
  • a sajt
  • az alma

In a sentence like this, a sajt can also sound natural in English as just cheese in a general sense, depending on context. Hungarian often uses the definite article where English may or may not.

Romlandó is an adjective meaning perishable, liable to spoil, or easily spoiled.

It comes from the verb romlik = to go bad / to spoil.

So:

• A sajt romlik. = The cheese is going bad / spoils.
• A sajt romlandó. = Cheese is perishable.

The form -andó / -endő often creates an adjective that expresses something like meant to, liable to, or to be ...-ed, depending on the word. Here it describes a property of the cheese.

Úgyhogy means so, therefore, or that’s why.

It connects a cause and a result:

• A sajt romlandó, úgyhogy...
• The cheese is perishable, so...

It is very common in spoken and written Hungarian for linking two clauses in a natural way.

A rough comparison:

• mert = because
• úgyhogy = so / therefore

For example:

• Mert romlandó, hűtőtáskába tesszük. = Because it’s perishable, we put it in a cooler bag.
• Romlandó, úgyhogy hűtőtáskába tesszük. = It’s perishable, so we put it in a cooler bag.

Because -ba / -be is the ending meaning into.

• hűtőtáska = cooler bag / insulated bag
• hűtőtáskába = into the cooler bag

This sentence uses movement into something, so Hungarian adds the case ending directly to the noun instead of using a separate word like into.

Compare:

• a hűtőtáskába = into the cooler bag
• a hűtőtáskában = in the cooler bag

So:

• tesszük a hűtőtáskába = we put it into the cooler bag
• not in the cooler bag as a static location, but into it

Because Hungarian keeps the article and the case ending.

So the structure is:

• a hűtőtáska = the cooler bag
• a hűtőtáskába = into the cooler bag

The article shows definiteness, and the ending shows grammatical role/location/direction.

This is very normal in Hungarian:

• a házban = in the house
• a boltba = into the shop
• a táskára = onto the bag

Tesszük is from the verb tesz = to put / to place / to do.

Here it means we put it.

More specifically, tesszük is:

• 1st person plural = we
• present tense
• definite conjugation

So:

• teszünk = we put / we do something indefinite or unspecified
• tesszük = we put it / we put the specific thing

Since the object is definite here — a sajt (the cheese) — Hungarian uses the definite conjugation on the verb.

That is one of the most important grammar points in Hungarian.

Because the thing being acted on is a specific, definite object: a sajt.

Hungarian verbs have two main conjugation patterns:

• indefinite
• definite

Use the definite one when the verb has a definite object, such as:

• a noun with a / az
• a pronoun like it, him, them
• a proper name in some contexts

Here:

• object = a sajt = the cheese
• therefore: tesszük, not teszünk

Compare:

• Sajtot teszünk a táskába. = We put cheese into the bag.
  (indefinite: some cheese / cheese in general)
• A sajtot a táskába tesszük. = We put the cheese into the bag.
  (definite: a specific cheese)

Hungarian often does not use a separate word for it when the object is already clear.

In this sentence, a sajt was already mentioned, so Hungarian can simply use the definite verb form tesszük, which already signals that a definite object is involved.

So English says:

• we put it in the cooler bag

Hungarian naturally says:

• a hűtőtáskába tesszük

If you wanted to say it explicitly, Hungarian could use azt, but that would usually sound more emphatic or contrastive:

• ...úgyhogy azt a hűtőtáskába tesszük.
• ...so we put that/it into the cooler bag.

In the original sentence, leaving it out is the most natural choice.

Both are possible, but the word order changes the focus.

Hungarian word order is flexible and often shows what is being emphasized.

• a hűtőtáskába tesszük puts focus on where we put it: into the cooler bag
• tesszük a hűtőtáskába is less focused and can sound more neutral in some contexts, but in this kind of sentence the preverbal element often carries emphasis

So the original sentence suggests something like:

• Since it’s perishable, we put it into the cooler bag
  (rather than somewhere else)

Hungarian very often places the most important new information right before the verb.

Yes. Hűtőtáska is a compound noun.

It is made of:

• hűtő = cooling / cooler / refrigerator
• táska = bag

Together:

• hűtőtáska = cooler bag, insulated bag, cool bag

This is very common in Hungarian: nouns are often built by combining two existing words into one compound.

Yes, but the structure and emphasis would change.

Original:

• A sajt romlandó, úgyhogy a hűtőtáskába tesszük.
• The cheese is perishable, so we put it in the cooler bag.

With mert:

• A hűtőtáskába tesszük, mert a sajt romlandó.
• We put it in the cooler bag because the cheese is perishable.

So:

• úgyhogy introduces the result
• mert introduces the reason

Both are natural, but they organize the information differently.