How can people possibly afford to live in one of the most expensive cities on the planet? It’s a question New Yorkers hear a lot, often delivered with a mix of awe, pity and confusion.

We surveyed hundreds of New Yorkers about how they spend, splurge and save. We found that many people — rich, poor or somewhere in between — live life as a series of small calculations that add up to one big question: What makes living in New York worth it?

Ernest Suarez loves everything about his job. He loves working with children with disabilities, scanning a room during a lesson to pick out which students may need to take a walk in the hallway or get some extra help later in the day. He loves the joyful chaos of recess.

He even loves his commute, especially on nice days, when he bikes from his home in the Norwood section of the Bronx over the Willis Avenue Bridge into Manhattan — which ends up saving him $6 a day in transit card swipes.

But his salary, $40,000, has made it difficult to support his three sons as the city he grew up in gets more and more expensive. Mr. Suarez’s wife, Michelle Suarez, 36, works at a nonprofit and made $45,000 last year.

Earlier this year, Mr. Suarez, 43, had a major surgery to remove a cancerous tumor from his spine. It took him months to get his disability payments, and his wife cut her hours to help take care of her bedridden husband. Mr. Suarez had never felt so financially squeezed and so grateful for his biweekly paycheck of $1,000 to kick back in after his medical leave.

Room and Board Times Two

The couple’s oldest son, John, who is 19 and preparing to enter the military, lives with them, as does their youngest, Jaxson, who recently turned 2.

They rent a two-bedroom apartment for $1,700 a month, and it’s tight with a toddler and a teenager. John has one bedroom, and the couple has the other.

When Jaxson was born, Mr. Suarez converted part of the living room into a nursery, wrapping it in a safari-themed wallpaper.

The couple’s middle son, Heaven, 18, is in his first year at a university upstate, near the Canadian border. Mr. Suarez and Ms. Suarez put aside a major chunk of their income, about $500 a month, to support Heaven, who is on a full scholarship and has an on-campus job, but still needs help with the cost of room and board.

The cost of keeping Heaven in college leaves very little left over after paying for rent and other necessities, including box after box of diapers for Jaxson.

“It’s a sacrifice,” Mr. Suarez said. “Money is on my mind a lot.”

Every Little Bit Counts

The couple were shocked when they toured nearby day cares and found that the prices had skyrocketed since their older sons needed child care. Mr. Suarez’s union, the United Federation of Teachers, offers a child care navigator that helps its members find which subsidies they are eligible for and which day cares have availability nearby. The couple qualified for a child care voucher, which allows them to pay $11 a week at day care that would otherwise cost $600.

The family spends between $100 and $150 a week on groceries from BJ’s or Stop & Shop, which they get through Instacart to save time.

They rarely eat out, but when they do splurge, they often go to Carmine’s in Times Square, where a plate of rigatoni with sausage and broccoli runs $39.95. The family also loves a day at their nearest movie theater, Regal Concourse, but tickets and snacks for everyone can cost $100 or more.

For truly special occasions, Mr. Suarez treats himself to a wrestling match at Madison Square Garden or the Barclays Center, but he almost never pays full price. Instead, he waits until the day before the event and then scrolls StubHub for cheaper tickets, which still means about $100 a head.

He usually takes one of his sons. “My wife doesn’t like it,” he said.

Keeping the Lights On

Mr. Suarez is one of the lowest paid members of his union, which is currently pushing the city to raise wages for paraprofessionals. But being a member of one of the city’s most powerful unions has major benefits.

When Mr. Suarez’s doctors found the tumor on his spine, the first estimate he received for a surgery to remove it was $177,000. After he applied his union insurance, the bill came down to about $100 total.

But the physical, mental and financial recovery from the procedure left Mr. Suarez reeling. The couple relied on his wife’s paychecks to keep the lights on as their electricity bill climbed to $140 a month following the coldest weeks of winter.

Mr. Suarez told his landlord he would have to be a month or two late on rent, and the landlord waived the usual late fee. He tried to apply for food stamp benefits, but found that his family didn’t qualify because their income last year was too high. He visited a few nearby food pantries to make sure his sons had enough to eat.

His first delayed disability check was so low that it only helped him get his bank account out of overdraft, and up to $5.

One of the toughest sacrifices was that the family could not afford to pay for Heaven to come home from college during spring break, because the round-trip bus ticket would have been close to $300.

By the spring, when Mr. Suarez was able to return to work, he knew his family needed something to lift their spirits after a brutal winter.

They surprised Jaxson, who is obsessed with animals, with a French bulldog puppy that a friend gave them.

Now the puppy, Oreo, sleeps right next to Jaxson’s crib every night. And when Jaxson wakes up in the morning, he tells Oreo he loves him and gives the dog a big hug. Mr. Suarez choked up as he described the new morning routine.

“That’s the end of the rainbow,” he said.