“Living quarters” is not the same term as a “quarter” that equals twenty-five cents. However, a hotel pun involving “quarters” has been popular since the 1890s. “No wonder we hate to pay the hotel clerk good dollars for poor quarters” was cited in a Minnesota newspaper in 1897.
 
“Rent is dollars for quarters” has been credited to Brooklyn-born Frank Tyger (1929-2011) an editorial cartoonist on the Trenton (NJ) Times from 1962 to 1996. It’s not known when Tyger’s line appeared in print. “Dollars for quarters” was a crossword clue in 1985; the four-letter answer was “rent.”
   
 
Welcome to the World of TYGER
Frank Tyger   -  A Brief Biography
Frank was born on December 24, 1929 in Brooklyn, New York to Belle and Joseph Tyger
(...)
In 1962 James Kerney Jr., then editor and publisher of The Trenton Times, offered Frank the job of his dreams—editorial cartoonist.  For the next 34 years, Frank worked for The Times drawing these cartoons, assuming other responsibilities including Promotion Manager, and writing a weekly Monday column for the paper.  During this time, he continued to pursue his lifelong interest in authoring quotes and puns which were published nationally in magazines such as Reader’s Digest, Forbes, Editor and Publisher and the Saturday Evening Post.
(...)
On May 2, 2011 Frank passed away after his 15-year battle with Parkinson’s Disease.
Frank Tyger—In His Own Words
Rent is dollars for quarters.
 
Chronicling America
28 July 1897, New Ulm (MN) Review, “Flashes of Wit,” pg. 4, col. 2:
No wonder we hate to pay the hotel clerk good dollars for poor quarters.
 
17 February 1898, National Labor Tribune (Pittsburgh, PA), “Sparks of Wit and Wisdom,” pg. 3, col. 4:
You can’t blame the hotel guest for kicking when he has to pay out good dollars for poor quarters.
 
Google Books
The Foolish Dictionary:
An Exhausting Work of Reference to Uncertain English Words, Their Origin, Meaning, Legitimate and Illegitimate Use
By Gideon Wurdz (pseudonym of Charles Wayland Towne—ed.)
Boston, MA: John W. Luce and Company
1904
Pg. ?:
HOTEL A place where a guest often gives up good dollars for poor quarters.
 
Google News Archive
31 January 1950, Prescott (AZ) Evening Courier, “Hassayampa Yamps” by the Old Cattleman and His Grapevine Friends, pg. 4, col. 2:
SOMETHING NOT TO WORRY about: Why a hotel is where one gives dollars for quarters.
 
4 January 1951, Cullman (AL) Banner, “Bama Bob,” pg. 6, col. 3:
Hotel—A place where a guest usually gives up good dollars for poor quarters.
   
Google Books
February 1955, Boys’ Life, “Think and Grin,” pg. 78, col. 2:
Daffynishion: Hotel — A place where you pay dollars for quarters. — Larry Ficklin, Tremonton, Utah.
 
22 June 1971, The Berkshire Eagle (Pittsfield, MA), pg. 9, col. 5 ad:
We have a good deal on dollars for quarters…
For your living quarters, that is.
(Mutual Savings Banks.—ed.)
 
18 August 1976, Grandview (Manitoba) Exponent, “Shooting the Breeze” by Ross Cairns, pg. 4, col. 2:
Hotel: A place where you trade dollars for quarters.
 
10 November 1978, San Diego (CA) Union, “Fun Time—The Riddle Box,”  pg. A-26, col. 2:
Where do you pay dollars for quarters?
A hotel.
 
7 March 1985, Brandon (Manitoba) Sun, “The Daily Crossword” by Mary Cee Whitten, pg. 18, col. 1:
ACROSS
60 Dollars for quarters
(“Rent” is the four-letter answer.—ed.)
 
14 May 1986, Medicine Hat (Alberta) News, pg. B5, col. 5:
Yesterday’s Cryptoquip: LANDLORDS WERE GETTING QUITE A FEW DOLLARS FOR QUARTERS.
 
Google Books
Kevin Ahern’s 1001 Punniest Limericks
By Kevin Ahern
Davinci Press (davincipress.com)
2014
Pg. 20:
We know they have many supporters
With customers staying as boarders
That’s the way that it is In the old hotel biz
Where patrons pay dollars for quarters. 
 
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Rent is dollars for quarters. #quote #franktyger
10:50 PM - 29 May 2015