The phrase "answers the purpose" is correct and usable in written English.
It can be used when indicating that something fulfills a specific need or requirement.
Example: "This solution answers the purpose of improving our workflow efficiency."
Alternatives: "serves the purpose" or "meets the objective".
I have written it for the use of emigrants more than for show, and if it answers the purpose of assisting them I shall be well satisfied.
"A proper name," Mill contended A System of Logic, is nothing more than "a word that answers the purpose of showing what thing it is that we are talking about, but not of telling anything about it".
This goal was espoused by the American Society of Civil Engineers, which opined, "That is the best engineering, not which makes the most splendid, or even the most perfect work, but that which makes a work that answers the purpose well, at the least cost".
They were informed about the goals and rules of the project and signed an informed consent approved by the local Helsinki Committee; however to avoid bias in answers, the purpose of the inquiry was explained them without mentioning its connection with a special atmospheric state.
But the greatest objection of all is, that the decisions which would probably result from such appeals, would not answer the purpose of maintaining the constitutional equilibrium of the government.
If the roof be of a moderate span, the ridge piece (columen), and rafters (cantherii), of sufficient projection at their feet to throw the water off the walls, will answer the purpose.
Good habits, imperceptibly fixed, are far preferable to the precepts of reason; but as this task requires more judgement than generally falls to the lot of parents, substitutes must be sought for, and medicines given, when regimen would have answered the purpose better'.
The Hereditary interest of the King was so interwoven with that of the Nation, and his personal emoluments so great, that he was placed above the danger of being corrupted from abroad--and at the same time was both sufficiently independent and sufficiently controuled, to answer the purpose of the institution at home.
