Learn Italian: Avete trentacinque euro. - You have thirty-five euros.

Yes, but not here! You drop the final vowel of the "tens" number only when the next number starts with a vowel—which means adding uno (one) or otto (eight). That gives us trentuno (thirty-one). Since cinque starts with a consonant, we keep the "a" in trentacinque.

Why doesn't the word euro change to euri for the plural?

The word euro is an exception to the normal plural rules in Italian. It never changes its ending. Whether you have one or thirty-five, it is always euro.

Why is "you have" translated as avete here instead of hai?

Avete is the plural "you have" (like "you all have" or "you guys have"). The English word "you" can be singular or plural, but this Italian sentence is specifically talking to more than one person. If you were speaking to just one person, you would use hai.