M: It's 100% silk, ma'am.

W: But I don't have enough money with me now.
M: How much do you have?
W: Thirty dollars, but I need two dollars for the bus.
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In this dialogue, what is the part of speech of 'for the bus'?
Is it an adjective phrase or an adver phrase? Does 'for the bus' modify 'dollars' or the verb 'need'?

Does it tell why "I need"?

If so, then it's adverbial.

Thank you. What about the follwing explanation?

1. I need two dollars which can be used for the bus.

2. I need two dollars used for the bus.

3. I need two dollars for the bus.

(If we explain in this way, can't 'for the bus' modify 'dollars'?)

Because "for the bus" is not telling what the dollars look like or are like. That phrase is not DESCRIBING the dollars.

However, it is answering one of the questions that adverbs are used for:
"Adverbs can be single words, or they can be phrases or clauses. Adverbs answer one of these four questions: How? When? Where? and Why?"
http://www.chompchomp.com/terms/adverb.htm

Thank you for our clarification.

To determine the part of speech of 'for the bus' and whether it functions as an adjective phrase or an adverb phrase, we need to look at how it is used in the sentence.

In the sentence "Thirty dollars, but I need two dollars for the bus," the phrase 'for the bus' is functioning as a prepositional phrase. Prepositional phrases are made up of a preposition and its object. In this case, the preposition is 'for' and its object is 'the bus'.

Prepositional phrases can function as adjectives or adverbs depending on how they modify other parts of the sentence. In this case, 'for the bus' is modifying the noun 'dollars'. It tells us the purpose or use of the two dollars, indicating that it is specifically for the bus fare. Therefore, 'for the bus' is functioning as an adjectival prepositional phrase, modifying the noun 'dollars'.

To summarize, the part of speech of 'for the bus' is a prepositional phrase, and it acts as an adjectival phrase, modifying the noun 'dollars'.