In todays Muslim world people recite different verses, Names of Allah or His Prophet (Sallallahu Alaihi wa Sallam), in different numbers and sequence to get certain benefits (i.e. increase in their wealth) or to get rid of some problems (i.e. marriage of their daughters) in their lifes. Is this action supported by any verse of Qur'an or by some Hadith or any of the Imams?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah Commands His slaves to ask only from Him and assures them that he responds them. Allah Says (interpretation of meaning): {And your Lord said: "Invoke Me, [i.e. believe in My Oneness (Islâmic Monotheism)] (and ask Me for anything) I will respond to your (invocation). …} [40: 60]. He also Says: {And when My slaves ask you (O Muhammad SAW) concerning Me, then (answer them), I am indeed near (to them by My Knowledge). I respond to the invocations of the supplicant when he calls on Me (without any mediator or intercessor). ….} [2: 186].
In another verse He Said: {And (all) the Most Beautiful Names belong to Allâh, so call on Him by them, …} [7: 180].
The Prophet (Sallallahu Alaihi wa Sallam) said: "Whenever you ask, ask Allah Alone, and whenever you seek help, should seek from Allah Alone" . [ Ahmad and al-Tirmizi ]. Anas (Radiya Allahu Anhu) reported from the Prophet (Sallallahu Alaihi wa Sallam) that he said: "Let one of you ask his Lord for all that he needs, even asking Him for salt, and even asking Him for his thong when it is cut" .
Allah Says (interpretation of meaning): {…, and ask Allah of His Bounty. …} [4: 32].
In the explanation of this verse Ayisha (Radiya Allahu Anha) said: "One should ask Allah even satiety since if He does not grant it one will never feel it" .
Therefore, a Muslim can ask Allah by His Names, Attributes, His Book (al-Qur'an) everything he needs if his asking does not include sin and severing of kinship relations.
As for reciting Names, Attributes of Allah, or some verses from Qur'an, one may do so not considering any fixed number. One may increase or decrease the number. So, abiding by certain numbers, believing that they could help in getting certain benefits such as a job, or save one from problems is not permissible unless there is evidence that proves so.
The matter of making Du'a by the names of the Prophet (Sallallahu Alaihi wa Sallam) is totally impermissible in Shari'a. The Prophet (Sallallahu Alaihi wa Sallam) made clear in the above Hadith that one should seek help only from Allah and should ask Him alone; Allah is all-Hearing, even near and Almighty; He fulfills the needs of people.
Allah knows best.