Learn Hardcore Czech: Kolik je ti let a kolik je tvojí sestře? - How old are you and how old is your sister?

Kolik – how many / how much
je – is
ti – to you (dative of ty)
let – of years (genitive plural of rok – year; the irregular plural form let)

So Kolik je ti let = How many years is to you? → idiomatically: How old are you?

Second part:

a – and
kolik – how many / how much
je – is
tvojí – your (feminine, dative; agreeing with sestře)
sestře – to (your) sister (dative of sestra – sister)

So kolik je tvojí sestře? = How many (years) is to your sister? → How old is your sister?
The word let is simply omitted in the second clause because it’s clear from context (see another question below).

Why is ti used here, and what case is it?

Ti is the unstressed (clitic) dative form of ty (you, singular informal).

Czech expresses age with the pattern:

je komu kolik let
(it is to someone how-many years)

So you say:

Je mi dvacet let. – It is to-me twenty years. → I am twenty.
Kolik je ti let? – How many years is to-you? → How old are you?

Here, ti answers the question Komu? (To whom?), which is the dative case.
The full, stressed form is tobě:

Kolik je tobě let? – also correct, but more emphatic; the neutral everyday version is Kolik je ti let?

Why is sestře in the dative case instead of the basic form sestra?

Same reason as with ti: the age construction uses the dative to mark the person whose age we’re talking about.

sestra – nominative (dictionary form)
sestře – dative singular

The pattern again is:

Je (komu?) kolik (čeho?) let.
It is (to whom?) how many (of what?) years.

So for your sister:

Kolik je tvojí sestře (let)?
How many years is to your sister? → How old is your sister?

Dative answers Komu? Čemu? (To whom? To what?), here (ke) sestře → sestře.

What exactly is tvojí, and why does it have that ending?

Tvojí is a form of the possessive adjective tvůj (your, singular informal).
Possessive adjectives agree with the noun they modify in gender, number and case.

Noun: sestra – feminine, singular
Case (because of the verb je with the age construction): dative
Feminine singular dative of tvůj can be:
- tvé sestře – more standard/literary
- tvojí sestře – very common in everyday spoken Czech

So:

tvojí sestře = to your sister (informal)
Formally both tvé sestře and tvojí sestře are used; many teachers and textbooks prefer tvé as more “textbook standard”, but tvojí is very frequent in speech.

Can I say Kolik je tobě let or Kolik je tvé sestře? Are these correct?

Yes, they are grammatically correct; they just differ in style or emphasis.

Kolik je tobě let?
- Uses the full stressed dative pronoun tobě.
- Emphasises you, like: How old are *you (as opposed to someone else)?*
- Neutral answer: Kolik je ti let? (clitic ti) is more typical in everyday speech.
Kolik je tvé sestře?
- Perfectly correct and a bit more “textbook”.
- Full version would be Kolik je tvé sestře let?, but let is often dropped if it’s clear from context.

So:

Neutral spoken: Kolik je ti let a kolik je tvojí sestře?
Slightly more formal/textbook: Kolik je tobě let a kolik je tvé sestře (let)?

Why is it Kolik je ti let and not something like Kolik máš let or Kolik let máš? Are those wrong?

They are not wrong, but they are less typical for neutral modern speech.

Native speakers most often use variants of je komu kolik let:

Kolik je ti let?
Kolik ti je? (shorter, very common)
Kolik je tvojí sestře? (with let optionally expressed)

Phrases with mít (to have) are understood and used, but they have a specific feel:

Kolik máš let? – correct, often used with children or in very simple speech, sometimes feels a bit “child-directed” or old-fashioned.
Kolik let máš? – also possible, similar feel.

If you want to sound most natural in everyday Czech, prefer:

Kolik je ti let? for “How old are you?”
Kolik ti je? – very common, casual.

Why is let missing in the second part: kolik je tvojí sestře? Where did “years” go?

It is understood from context and simply omitted to avoid repetition, a very common thing in Czech.

Full, explicit version would be:

Kolik je ti let a kolik je tvojí sestře let?

Since let appears in the first clause, native speakers normally drop it in the second:

Kolik je ti let a kolik je tvojí sestře?

You can safely omit repeated words when the meaning is obvious, especially in coordinated clauses like this.

Would Kolik let je ti a kolik let je tvojí sestře? also be correct? Does the word order change the meaning?

Yes, Kolik let je ti a kolik let je tvojí sestře? is grammatically correct.

Czech has flexible word order, and the main rules here are:

The clitic ti tends to appear in the second position in the clause, which both
Kolik je ti let? and Kolik let je ti? respect.
Putting let earlier (as in Kolik let je ti?) slightly emphasizes years, but the meaning is the same.

All of these are acceptable:

Kolik je ti let? – most common, neutral.
Kolik let je ti? – also okay, a bit more marked in word order.
Kolik je tvojí sestře (let)? – standard for the sister part.

So you can say Kolik let je ti a kolik let je tvojí sestře?, but the original order is more typical in everyday use.

Why is the verb je in the singular when we’re talking about multiple years?

The agreement is not with years, but with the impersonal/quantitative structure.

The pattern:

Je mi dvacet let. – literally: It is to-me twenty of-years.

Here:

je is 3rd person singular (like English is)
The phrase dvacet let is a quantity expression, not a grammatical subject controlling agreement.

In Kolik je ti let?

Kolik (how many) behaves like a neuter singular interrogative pronoun for quantities.
Verb je (3rd person singular) matches that.

So you always say:

Je mi pět let. – I am five.
Je mu třicet. – He is thirty.
Kolik je ti let? – How old are you?

Never jsou mi pět let; that would be wrong.

Why can’t I just say Kolik je tvoje sestra? to mean “How old is your sister?”

Because in Czech je (is) normally needs either:

a predicate adjective or noun:
- Moje sestra je mladá. – My sister is young.
- Moje sestra je učitelka. – My sister is a teacher.

or a quantity/age construction with let and dative.

Kolik je tvoje sestra? literally sounds like:

How much is your sister? or How many is your sister?

It is ungrammatical and does not convey age in Czech.
You must use the age construction:

Kolik je tvojí sestře (let)? – How old is your sister?
or simply:
Kolik jí je? – How old is she? (using only the pronoun).

How would I say this politely/formally to an adult I don’t know well?

Use vy-forms (formal “you”) and the corresponding possessive:

Kolik je vám let a kolik je vaší sestře?

Breakdown of formal forms:

vám – dative of formal vy (to you, polite)
vaší – formal “your”, feminine dative (agreeing with sestře)
vaší sestře – to your sister (formal)

So:

Informal: Kolik je ti let a kolik je tvojí sestře?
Formal: Kolik je vám let a kolik je vaší sestře?

Is the word order fixed, or can I move ti, tvojí, and sestře around?

Word order is partly flexible, but clitics and emphasis matter.

Key points:

Clitic pronouns like ti want to be in second position in the clause:
- Kolik je ti let? – natural
- Kolik ti je let? – also possible
- Ti kolik je let? – wrong; ti shouldn’t start the clause.
In the second clause, you keep a natural order:
- Kolik je tvojí sestře? – most natural
- Kolik je sestře tvojí? – possible but unusual, sounds marked/poetic.

Good, natural options:

Kolik je ti let a kolik je tvojí sestře? – very natural.
Kolik ti je a kolik je tvojí sestře? – shorter, also very common.

So you can move some elements for emphasis, but:

keep ti in second position,
keep tvojí close to sestře,
and use the patterns you hear most often to sound natural.